Solve (x+2)^2-(x-4)^2=11x-8

$$( x + 2 ) ^ { 2 } - ( x - 4 ) ^ { 2 } = 11 x - 8$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

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

$$x^{2}+4x+4-\left(x-4\right)^{2}=11x-8$$

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

$$x^{2}+4x+4-\left(x^{2}-8x+16\right)=11x-8$$

To find the opposite of x^{2}-8x+16, find the opposite of each term.

$$x^{2}+4x+4-x^{2}+8x-16=11x-8$$

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

$$4x+4+8x-16=11x-8$$

Combine 4x and 8x to get 12x.

$$12x+4-16=11x-8$$

Subtract 16 from 4 to get -12.

$$12x-12=11x-8$$

Subtract 11x from both sides.

$$12x-12-11x=-8$$

Combine 12x and -11x to get x.

$$x-12=-8$$

Add 12 to both sides.

$$x=-8+12$$

Add -8 and 12 to get 4.

$$x=4$$