Solve 3(2-x)(x+2)=x^2

$$3 ( 2 - x ) ( x + 2 ) = x ^ { 2 }$$

Solve for x

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

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

$$\left(6-3x\right)\left(x+2\right)=x^{2}$$

Use the distributive property to multiply 6-3x by x+2 and combine like terms.

$$12-3x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$12-3x^{2}-x^{2}=0$$

Combine -3x^{2} and -x^{2} to get -4x^{2}.

$$12-4x^{2}=0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$-4x^{2}=-12$$

Divide both sides by -4.

$$x^{2}=\frac{-12}{-4}$$

Divide -12 by -4 to get 3.

$$x^{2}=3$$

Take the square root of both sides of the equation.

$$x=\sqrt{3} x=-\sqrt{3}$$

Steps Using the Quadratic Formula

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

$$\left(6-3x\right)\left(x+2\right)=x^{2}$$

Use the distributive property to multiply 6-3x by x+2 and combine like terms.

$$12-3x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$12-3x^{2}-x^{2}=0$$

Combine -3x^{2} and -x^{2} to get -4x^{2}.

$$12-4x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-4x^{2}+12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and 12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 12}}{2\left(-4\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4\right)\times 12}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$x=\frac{0±\sqrt{16\times 12}}{2\left(-4\right)}$$

Multiply 16 times 12.

$$x=\frac{0±\sqrt{192}}{2\left(-4\right)}$$

Take the square root of 192.

$$x=\frac{0±8\sqrt{3}}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±8\sqrt{3}}{-8}$$

Now solve the equation x=\frac{0±8\sqrt{3}}{-8} when ± is plus.

$$x=-\sqrt{3}$$

Now solve the equation x=\frac{0±8\sqrt{3}}{-8} when ± is minus.

$$x=\sqrt{3}$$

The equation is now solved.

$$x=-\sqrt{3} x=\sqrt{3}$$