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

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

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

$x=-3$

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:

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

$x=5$

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

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

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

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:

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

$x=-13$