Solve x(x-3-2)/2=left(x-3right)x/2-19

$$\frac{ x(x-3-2) }{ 2 } = \frac{ \left( x-3 \right) x }{ 2 } -19$$

Solve for x

$$x=19$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$x\left(x-3-2\right)=\left(x-3\right)x-38$$

Subtract 2 from -3 to get -5.

$$x\left(x-5\right)=\left(x-3\right)x-38$$

Use the distributive property to multiply x by x-5.

$$x^{2}-5x=\left(x-3\right)x-38$$

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

$$x^{2}-5x=x^{2}-3x-38$$

Subtract x^{2} from both sides.

$$x^{2}-5x-x^{2}=-3x-38$$

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

$$-5x=-3x-38$$

Add 3x to both sides.

$$-5x+3x=-38$$

Combine -5x and 3x to get -2x.

$$-2x=-38$$

Divide both sides by -2.

$$x=\frac{-38}{-2}$$

Divide -38 by -2 to get 19.

$$x=19$$