Solve (x-4)^2-4=(x-6)(x-8)

$$( x - 4 ) ^ { 2 } - 4 = ( x - 6 ) ( x - 8 )$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

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

$$x^{2}-8x+16-4=\left(x-6\right)\left(x-8\right)$$

Subtract 4 from 16 to get 12.

$$x^{2}-8x+12=\left(x-6\right)\left(x-8\right)$$

Use the distributive property to multiply x-6 by x-8 and combine like terms.

$$x^{2}-8x+12=x^{2}-14x+48$$

Subtract x^{2} from both sides.

$$x^{2}-8x+12-x^{2}=-14x+48$$

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

$$-8x+12=-14x+48$$

Add 14x to both sides.

$$-8x+12+14x=48$$

Combine -8x and 14x to get 6x.

$$6x+12=48$$

Subtract 12 from both sides.

$$6x=48-12$$

Subtract 12 from 48 to get 36.

$$6x=36$$

Divide both sides by 6.

$$x=\frac{36}{6}$$

Divide 36 by 6 to get 6.

$$x=6$$