Solve 14-(6-x)*(6-x)=x(2-x)

$$14-(6-x) \times (6-x)=x(2-x)$$

Solve for x

$$x = \frac{11}{5} = 2\frac{1}{5} = 2.2$$

Steps for Solving Linear Equation

Multiply 6-x and 6-x to get \left(6-x\right)^{2}.

$$14-\left(6-x\right)^{2}=x\left(2-x\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6-x\right)^{2}.

$$14-\left(36-12x+x^{2}\right)=x\left(2-x\right)$$

To find the opposite of 36-12x+x^{2}, find the opposite of each term.

$$14-36+12x-x^{2}=x\left(2-x\right)$$

Subtract 36 from 14 to get -22.

$$-22+12x-x^{2}=x\left(2-x\right)$$

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

$$-22+12x-x^{2}=2x-x^{2}$$

Subtract 2x from both sides.

$$-22+12x-x^{2}-2x=-x^{2}$$

Combine 12x and -2x to get 10x.

$$-22+10x-x^{2}=-x^{2}$$

Add x^{2} to both sides.

$$-22+10x-x^{2}+x^{2}=0$$

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

$$-22+10x=0$$

Add 22 to both sides. Anything plus zero gives itself.

$$10x=22$$

Divide both sides by 10.

$$x=\frac{22}{10}$$

Reduce the fraction \frac{22}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{11}{5}$$