Solve left(x+6right)left(x-6right)-x(x-9)=0

$$\left( x+6 \right) \left( x-6 \right) -x(x-9)=0$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Consider \left(x+6\right)\left(x-6\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 6.

$$x^{2}-36-x\left(x-9\right)=0$$

Use the distributive property to multiply x by x-9.

$$x^{2}-36-\left(x^{2}-9x\right)=0$$

To find the opposite of x^{2}-9x, find the opposite of each term.

$$x^{2}-36-x^{2}+9x=0$$

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

$$-36+9x=0$$

Add 36 to both sides. Anything plus zero gives itself.

$$9x=36$$

Divide both sides by 9.

$$x=\frac{36}{9}$$

Divide 36 by 9 to get 4.

$$x=4$$