Solve (x+3)(2x-3)-6x=(x-4)(2x+4)+12

$$( x + 3 ) ( 2 x - 3 ) - 6 x = ( x - 4 ) ( 2 x + 4 ) + 12$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+3 by 2x-3 and combine like terms.

$$2x^{2}+3x-9-6x=\left(x-4\right)\left(2x+4\right)+12$$

Combine 3x and -6x to get -3x.

$$2x^{2}-3x-9=\left(x-4\right)\left(2x+4\right)+12$$

Use the distributive property to multiply x-4 by 2x+4 and combine like terms.

$$2x^{2}-3x-9=2x^{2}-4x-16+12$$

Add -16 and 12 to get -4.

$$2x^{2}-3x-9=2x^{2}-4x-4$$

Subtract 2x^{2} from both sides.

$$2x^{2}-3x-9-2x^{2}=-4x-4$$

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

$$-3x-9=-4x-4$$

Add 4x to both sides.

$$-3x-9+4x=-4$$

Combine -3x and 4x to get x.

$$x-9=-4$$

Add 9 to both sides.

$$x=-4+9$$

Add -4 and 9 to get 5.

$$x=5$$