Solve x^2-5x+15=xleft(x-3right)-14+5left(x-2right)+3(13-2x)

$${ x }^{ 2 } -5x+15 = x \left( x-3 \right) -14+5 \left( x-2 \right) +3(13-2x)$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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

$$x^{2}-5x+15=x^{2}-3x-14+5\left(x-2\right)+3\left(13-2x\right)$$

Use the distributive property to multiply 5 by x-2.

$$x^{2}-5x+15=x^{2}-3x-14+5x-10+3\left(13-2x\right)$$

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

$$x^{2}-5x+15=x^{2}+2x-14-10+3\left(13-2x\right)$$

Subtract 10 from -14 to get -24.

$$x^{2}-5x+15=x^{2}+2x-24+3\left(13-2x\right)$$

Use the distributive property to multiply 3 by 13-2x.

$$x^{2}-5x+15=x^{2}+2x-24+39-6x$$

Add -24 and 39 to get 15.

$$x^{2}-5x+15=x^{2}+2x+15-6x$$

Combine 2x and -6x to get -4x.

$$x^{2}-5x+15=x^{2}-4x+15$$

Subtract x^{2} from both sides.

$$x^{2}-5x+15-x^{2}=-4x+15$$

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

$$-5x+15=-4x+15$$

Add 4x to both sides.

$$-5x+15+4x=15$$

Combine -5x and 4x to get -x.

$$-x+15=15$$

Subtract 15 from both sides.

$$-x=15-15$$

Subtract 15 from 15 to get 0.

$$-x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -1 is not equal to 0, x must be equal to 0.

$$x=0$$