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

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

Solve for x

$$x=2$$

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}.

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

Use the distributive property to multiply 4 by x^{2}+4x+4.

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

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

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

Calculate 8 to the power of 2 and get 64.

$$4x^{2}+16x+16=16-16x+4x^{2}+64$$

Add 16 and 64 to get 80.

$$4x^{2}+16x+16=80-16x+4x^{2}$$

Add 16x to both sides.

$$4x^{2}+16x+16+16x=80+4x^{2}$$

Combine 16x and 16x to get 32x.

$$4x^{2}+32x+16=80+4x^{2}$$

Subtract 4x^{2} from both sides.

$$4x^{2}+32x+16-4x^{2}=80$$

Combine 4x^{2} and -4x^{2} to get 0.

$$32x+16=80$$

Subtract 16 from both sides.

$$32x=80-16$$

Subtract 16 from 80 to get 64.

$$32x=64$$

Divide both sides by 32.

$$x=\frac{64}{32}$$

Divide 64 by 32 to get 2.

$$x=2$$