Solve left(x+6right)^2=left(x-4right)^2

$${ \left(x+6 \right) }^{ 2 } = { \left(x-4 \right) }^{ 2 }$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$x^{2}+12x+36=\left(x-4\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$x^{2}+12x+36=x^{2}-8x+16$$

Subtract x^{2} from both sides.

$$x^{2}+12x+36-x^{2}=-8x+16$$

Combine x^{2} and -x^{2} to get 0.

$$12x+36=-8x+16$$

Add 8x to both sides.

$$12x+36+8x=16$$

Combine 12x and 8x to get 20x.

$$20x+36=16$$

Subtract 36 from both sides.

$$20x=16-36$$

Subtract 36 from 16 to get -20.

$$20x=-20$$

Divide both sides by 20.

$$x=\frac{-20}{20}$$

Divide -20 by 20 to get -1.

$$x=-1$$