Solve (x-3)*(2x-5)+4*(2-x)+12=2*(1-x)^2

$$( x - 3 ) \cdot ( 2 x - 5 ) + 4 \cdot ( 2 - x ) + 12 = 2 \cdot ( 1 - x ) ^ { 2 }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-3 by 2x-5 and combine like terms.

$$2x^{2}-11x+15+4\left(2-x\right)+12=2\left(1-x\right)^{2}$$

Use the distributive property to multiply 4 by 2-x.

$$2x^{2}-11x+15+8-4x+12=2\left(1-x\right)^{2}$$

Add 15 and 8 to get 23.

$$2x^{2}-11x+23-4x+12=2\left(1-x\right)^{2}$$

Combine -11x and -4x to get -15x.

$$2x^{2}-15x+23+12=2\left(1-x\right)^{2}$$

Add 23 and 12 to get 35.

$$2x^{2}-15x+35=2\left(1-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-x\right)^{2}.

$$2x^{2}-15x+35=2\left(1-2x+x^{2}\right)$$

Use the distributive property to multiply 2 by 1-2x+x^{2}.

$$2x^{2}-15x+35=2-4x+2x^{2}$$

Add 4x to both sides.

$$2x^{2}-15x+35+4x=2+2x^{2}$$

Combine -15x and 4x to get -11x.

$$2x^{2}-11x+35=2+2x^{2}$$

Subtract 2x^{2} from both sides.

$$2x^{2}-11x+35-2x^{2}=2$$

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

$$-11x+35=2$$

Subtract 35 from both sides.

$$-11x=2-35$$

Subtract 35 from 2 to get -33.

$$-11x=-33$$

Divide both sides by -11.

$$x=\frac{-33}{-11}$$

Divide -33 by -11 to get 3.

$$x=3$$