Solve left(x-5right)left(x-2right)-left(x-1right)left(x+4right)=14

$$\left( x-5 \right) \left( x-2 \right) - \left( x-1 \right) \left( x+4 \right) =14$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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

$$x^{2}-7x+10-\left(x-1\right)\left(x+4\right)=14$$

Use the distributive property to multiply x-1 by x+4 and combine like terms.

$$x^{2}-7x+10-\left(x^{2}+3x-4\right)=14$$

To find the opposite of x^{2}+3x-4, find the opposite of each term.

$$x^{2}-7x+10-x^{2}-3x+4=14$$

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

$$-7x+10-3x+4=14$$

Combine -7x and -3x to get -10x.

$$-10x+10+4=14$$

Add 10 and 4 to get 14.

$$-10x+14=14$$

Subtract 14 from both sides.

$$-10x=14-14$$

Subtract 14 from 14 to get 0.

$$-10x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -10 is not equal to 0, x must be equal to 0.

$$x=0$$