Solve (x-3)(x+4)-2(3x-2)=(x-4)^2

$$( x - 3 ) ( x + 4 ) - 2 ( 3 x - 2 ) = ( x - 4 ) ^ { 2 }$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-3 by x+4 and combine like terms.

$$x^{2}+x-12-2\left(3x-2\right)=\left(x-4\right)^{2}$$

Use the distributive property to multiply -2 by 3x-2.

$$x^{2}+x-12-6x+4=\left(x-4\right)^{2}$$

Combine x and -6x to get -5x.

$$x^{2}-5x-12+4=\left(x-4\right)^{2}$$

Add -12 and 4 to get -8.

$$x^{2}-5x-8=\left(x-4\right)^{2}$$

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

$$x^{2}-5x-8=x^{2}-8x+16$$

Subtract x^{2} from both sides.

$$x^{2}-5x-8-x^{2}=-8x+16$$

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

$$-5x-8=-8x+16$$

Add 8x to both sides.

$$-5x-8+8x=16$$

Combine -5x and 8x to get 3x.

$$3x-8=16$$

Add 8 to both sides.

$$3x=16+8$$

Add 16 and 8 to get 24.

$$3x=24$$

Divide both sides by 3.

$$x=\frac{24}{3}$$

Divide 24 by 3 to get 8.

$$x=8$$