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

$$( 1 - x ) ( 2 - x ) = ( x + 3 ) ( x - 4 )$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

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

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

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

$$2-3x+x^{2}=x^{2}-x-12$$

Subtract x^{2} from both sides.

$$2-3x+x^{2}-x^{2}=-x-12$$

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

$$2-3x=-x-12$$

Add x to both sides.

$$2-3x+x=-12$$

Combine -3x and x to get -2x.

$$2-2x=-12$$

Subtract 2 from both sides.

$$-2x=-12-2$$

Subtract 2 from -12 to get -14.

$$-2x=-14$$

Divide both sides by -2.

$$x=\frac{-14}{-2}$$

Divide -14 by -2 to get 7.

$$x=7$$