Solving Quadratic Equations using Factoring: Equations with variables on both sides

Solve for x:

$7(-2x+5)=77$

To open parentheses we will use the formula:

$a(x+b)=ax+ab$

$(7\times-2x)+(7\times5)=77$

We multiply accordingly

$-14x+35=77$

We will move the 35 to the right section and change the sign accordingly:

$-14x=77-35$

We solve the subtraction exercise on the right side and we will obtain:

$-14x=42$

We divide both sections by -14

$\frac{-14x}{-14}=\frac{42}{-14}$

$x=-3$

-3

Solve for x:

$-9(2-x)=(x+4)\cdot3$

We open the parentheses in both sections by the distributive property and use the formula:

$a(x+b)=ax+ab$

$-18+9x=3x+12$

We move 3X to the left section, and 18 to the right section and maintain the corresponding signs:

$9x-3x=12+18$

We add the terms:

$6x=30$

We divide both sections by 6:

$\frac{6x}{6}=\frac{30}{6}$

$x=5$

5

Solve for x:

$-8(2x+4)=6(x-4)+3$

To open parentheses we will use the formula:

$a\left(x+b\right)=ax+ab$

$(-8\times2x)+(-8\times4)=(6\times x)+(6\times-4)+3$

We multiply accordingly:

$-16x-32=6x-24+3$

Calculate the elements on the right section:

$-16x-32=6x-21$

In the left section we enter the elements with the X and in the left section those without the X, remember to change the plus and minus signs as appropriate when transferring:

$-32+21=6x+16x$

Calculate the elements accordingly

$-11=22x$

We divide the two sections by 22

$-\frac{11}{22}=\frac{22x}{22}$

$-\frac{1}{2}=x$

$-\frac{1}{2}$

Solve for x:

$-7(2x+3)-4(x+2)=5(2-3x)$

To open parentheses we will use the formula:

$a\left(x+b\right)=ax+ab$

$(-7\times2x)+(-7\times3)+(-4\times x)+(-4\times2)=(5\times2)+(5\times-3x)$

We multiply accordingly:

$-14x-21-4x-8=10-15x$

We calculate the elements in the left section:

$-18x-29=10-15x$

In the left section we enter the elements with the X and in the right section those without the X, remember to change the plus and minus signs as appropriate when transferring:

$-18x+15x=10+29$

We calculate the elements accordingly:

$-3x=39$

We divide the two sections by -3:

$\frac{-3x}{-3}=\frac{39}{-3}$

$x=-13$

-13

$3(b-1)-4(-b+3)=-28$

$-1\frac{6}{7}$

$2(x-4)+6(x+2)=-18$

$-2\frac{3}{4}$

$(y-5)-6(3+y)=7$

$-6$

Solve for x:

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

There is no solution.

Solve for x:

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

-20

Solve for x:

$-2(3x+2)+1=3(x+8)$

-3

Solve for x:

$(x-4)\cdot3=2(x+6)$

$24$

Solve for X:

$-8(4-x)+4(2x+5)=2(7-2x)$

$\frac{13}{10}$

Solve for X:

$-2(4-3x)+4(2x-4)=8(2-x)$

$\frac{20}{11}$

Solve for X:

$-2(4+5x)+3(2-2x)=8(4-x)$

$-\frac{17}{4}$

$(\frac{1}{2}x+3)-(4x+7)=1$

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