Solving Quadratic Equations using Factoring: Solving an equation using all techniques

Question 1

$$ -3(4a+8)=27a $$

$a=\text{?}$

Question 2

Solve for X:

$\frac{1}{2}(x+3)-8x=3$

Question 3

Solve for X:

$5(x-8)+\frac{1}{2}=0$

Question 4

Solve for X:

$-8(2-x)=\frac{1}{2}+x$

Question 5

$$ 6c+7+4c=3(c-1) $$

$c=\text{?}$

Examples with solutions for Solving Quadratic Equations using Factoring: Solving an equation using all techniques

Exercise #1

$-3(4a+8)=27a$

$a=\text{?}$

Video Solution

Step-by-Step Solution

To open the parentheses on the left side, we'll use the formula:

$-a\left(b+c\right)=-ab-ac$

$-12a-24=27a$

We'll arrange the equation so that the terms with 'a' are on the right side, and maintain the plus and minus signs during the transfer:

$-24=27a+12a$

Let's group the terms on the right side:

$-24=39a$

Let's divide both sides by 39:

$-\frac{24}{39}=\frac{39a}{39}$

$-\frac{24}{39}=a$

Note that we can reduce the fraction since both numerator and denominator are divisible by 3:

$-\frac{8}{13}=a$

Answer

$-\frac{8}{13}$

Exercise #2

Solve for X:

$\frac{1}{2}(x+3)-8x=3$

Video Solution

Answer

$-\frac{1}{5}$

Exercise #3

Solve for X:

$5(x-8)+\frac{1}{2}=0$

Video Solution

Answer

$\frac{79}{10}$

Exercise #4

Solve for X:

$-8(2-x)=\frac{1}{2}+x$

Video Solution

Answer

$\frac{33}{14}$

Exercise #5

$6c+7+4c=3(c-1)$

$c=\text{?}$

Video Solution

Answer

$-1\frac{3}{7}$

Question 1

$$ 7y+10y+5=2(y+3) $$

$y=\text{?}$

Question 2

Solve for X:

$-\frac{1}{2}(x-\frac{1}{4})=\frac{1}{2}(3-x)$

Question 3

Solve for X:

$\frac{1}{6}(x-4)=\frac{1}{4}(\frac{1}{3}x+3)$

Question 4

Solve for X:

$\frac{1}{8}(\frac{1}{2}-x)=\frac{1}{4}(x-\frac{1}{4})$

Question 5

$3x+\frac{2}{3}=4(x+\frac{1}{12})$

$x=\text{?}$

Exercise #6

$7y+10y+5=2(y+3)$

$y=\text{?}$

Video Solution

Answer

$\frac{1}{15}$

Exercise #7

Solve for X:

$-\frac{1}{2}(x-\frac{1}{4})=\frac{1}{2}(3-x)$

Video Solution

Answer

There is no solution.

Exercise #8

Solve for X:

$\frac{1}{6}(x-4)=\frac{1}{4}(\frac{1}{3}x+3)$

Video Solution

Answer

Exercise #9

Solve for X:

$\frac{1}{8}(\frac{1}{2}-x)=\frac{1}{4}(x-\frac{1}{4})$

Video Solution

Answer

Exercise #10

$3x+\frac{2}{3}=4(x+\frac{1}{12})$

$x=\text{?}$

Video Solution

Answer

$\frac{1}{3}$

Question 1

$$ 16a-20a+15=2(5-2a) $$

$a=\text{?}$

Question 2

$2x+45-\frac{1}{3}x=5(x+7)$

$x=\text{?}$

Question 3

$-\frac{7}{4}(-x)+2x-5(x+3)=-x$

$x=\text{?}$

Question 4

Solve for X:

$$ 8(x+3)-1+4x=8(x+3)-5(x-4) $$

Question 5

Solve for X:

$(5-x)\cdot\frac{1}{2}+3x-4(x-2)=\frac{1}{2}(x+4)$

Exercise #11

$16a-20a+15=2(5-2a)$

$a=\text{?}$

Video Solution

Answer

No solution

Exercise #12

$2x+45-\frac{1}{3}x=5(x+7)$

$x=\text{?}$

Video Solution

Answer

Exercise #13

$-\frac{7}{4}(-x)+2x-5(x+3)=-x$

$x=\text{?}$

Video Solution

Answer

$-60$

Exercise #14

Solve for X:

$8(x+3)-1+4x=8(x+3)-5(x-4)$

Video Solution

Answer

$\frac{7}{3}$

Exercise #15

Solve for X:

$(5-x)\cdot\frac{1}{2}+3x-4(x-2)=\frac{1}{2}(x+4)$

Video Solution

Answer

$\frac{17}{4}$

Question 1

$150+75m+\frac{m}{8}-\frac{m}{3}=(900-\frac{5m}{2})\cdot\frac{1}{12}$

$m=\text{?}$

Question 2

$$ -t+2(4+t)(t+5)=(t-5)(2t-3) $$

$t=\text{?}$

Question 3

$$ $$ (x+2)(2x-4)=2x^2+x+10 $$

Question 4

$(x+4)(3x-\frac{1}{4})=3(x^2+5)$

$$ x=? $$

Question 5

$$ -4(x^2+5)=(-x+7)(4x-9)+5 $$

$$ x=? $$

Exercise #16

$150+75m+\frac{m}{8}-\frac{m}{3}=(900-\frac{5m}{2})\cdot\frac{1}{12}$

$m=\text{?}$

Video Solution

Answer

$-1$

Exercise #17

$-t+2(4+t)(t+5)=(t-5)(2t-3)$

$t=\text{?}$

Video Solution

Answer

$-\frac{5}{6}$

Exercise #18

$(x+2)(2x-4)=2x^2+x+10$

Video Solution

Answer

$-18$

Exercise #19

$(x+4)(3x-\frac{1}{4})=3(x^2+5)$

$x=?$

Video Solution

Answer

$1\frac{17}{47}$

Exercise #20

$-4(x^2+5)=(-x+7)(4x-9)+5$

$x=?$

Video Solution

Answer

$1\frac{1}{37}$