Solve 12-left(4-xright)^2=x(3-x)

$$12- { \left(4-x \right) }^{ 2 } =x(3-x)$$

Solve for x

$$x=\frac{4}{5}=0.8$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4-x\right)^{2}.

$$12-\left(16-8x+x^{2}\right)=x\left(3-x\right)$$

To find the opposite of 16-8x+x^{2}, find the opposite of each term.

$$12-16+8x-x^{2}=x\left(3-x\right)$$

Subtract 16 from 12 to get -4.

$$-4+8x-x^{2}=x\left(3-x\right)$$

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

$$-4+8x-x^{2}=3x-x^{2}$$

Subtract 3x from both sides.

$$-4+8x-x^{2}-3x=-x^{2}$$

Combine 8x and -3x to get 5x.

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

Add x^{2} to both sides.

$$-4+5x-x^{2}+x^{2}=0$$

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

$$-4+5x=0$$

Add 4 to both sides. Anything plus zero gives itself.

$$5x=4$$

Divide both sides by 5.

$$x=\frac{4}{5}$$