Solve (3x-2)^2-3x(x-4)=(2x-1)(3x+2)

$$( 3 x - 2 ) ^ { 2 } - 3 x ( x - 4 ) = ( 2 x - 1 ) ( 3 x + 2 )$$

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(3x-2\right)^{2}.

$$9x^{2}-12x+4-3x\left(x-4\right)=\left(2x-1\right)\left(3x+2\right)$$

Use the distributive property to multiply 2x-1 by 3x+2 and combine like terms.

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

Subtract 6x^{2} from both sides.

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

Subtract x from both sides.

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

Use the distributive property to multiply -3x by x-4.

$$9x^{2}-12x+4-3x^{2}+12x-6x^{2}-x=-2$$

Combine 9x^{2} and -3x^{2} to get 6x^{2}.

$$6x^{2}-12x+4+12x-6x^{2}-x=-2$$

Combine -12x and 12x to get 0.

$$6x^{2}+4-6x^{2}-x=-2$$

Combine 6x^{2} and -6x^{2} to get 0.

$$4-x=-2$$

Subtract 4 from both sides.

$$-x=-2-4$$

Subtract 4 from -2 to get -6.

$$-x=-6$$

Multiply both sides by -1.

$$x=6$$