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

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

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

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

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

$$4x^{2}-12x+9-\left(3x^{2}-5x+2\right)=\left(3-x\right)^{2}$$

To find the opposite of 3x^{2}-5x+2, find the opposite of each term.

$$4x^{2}-12x+9-3x^{2}+5x-2=\left(3-x\right)^{2}$$

Combine 4x^{2} and -3x^{2} to get x^{2}.

$$x^{2}-12x+9+5x-2=\left(3-x\right)^{2}$$

Combine -12x and 5x to get -7x.

$$x^{2}-7x+9-2=\left(3-x\right)^{2}$$

Subtract 2 from 9 to get 7.

$$x^{2}-7x+7=\left(3-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3-x\right)^{2}.

$$x^{2}-7x+7=9-6x+x^{2}$$

Add 6x to both sides.

$$x^{2}-7x+7+6x=9+x^{2}$$

Combine -7x and 6x to get -x.

$$x^{2}-x+7=9+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-x+7-x^{2}=9$$

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

$$-x+7=9$$

Subtract 7 from both sides.

$$-x=9-7$$

Subtract 7 from 9 to get 2.

$$-x=2$$

Multiply both sides by -1.

$$x=-2$$