Solve 3x^2+12x+24x=0

$$3 { x }^{ 2 } +12x+24x=0$$

Solve for x

$$x=-12$$

$$x=0$$

Steps Using Factoring

Factor out x.

$$x\left(3x+12+24\right)=0$$

To find equation solutions, solve x=0 and 3x+36=0.

$$x=0 x=-12$$

Steps Using the Quadratic Formula

Combine 12x and 24x to get 36x.

$$3x^{2}+36x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 36 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-36±\sqrt{36^{2}}}{2\times 3}$$

Take the square root of 36^{2}.

$$x=\frac{-36±36}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{-36±36}{6}$$

Now solve the equation x=\frac{-36±36}{6} when ± is plus. Add -36 to 36.

$$x=\frac{0}{6}$$

Divide 0 by 6.

$$x=0$$

Now solve the equation x=\frac{-36±36}{6} when ± is minus. Subtract 36 from -36.

$$x=-\frac{72}{6}$$

Divide -72 by 6.

$$x=-12$$

The equation is now solved.

$$x=0 x=-12$$

Steps for Completing the Square

Combine 12x and 24x to get 36x.

$$3x^{2}+36x=0$$

Divide both sides by 3.

$$\frac{3x^{2}+36x}{3}=\frac{0}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x^{2}+\frac{36}{3}x=\frac{0}{3}$$

Divide 36 by 3.

$$x^{2}+12x=\frac{0}{3}$$

Divide 0 by 3.

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

Divide 12, the coefficient of the x term, by 2 to get 6. Then add the square of 6 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+12x+6^{2}=6^{2}$$

Square 6.

$$x^{2}+12x+36=36$$

Factor x^{2}+12x+36. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+6\right)^{2}=36$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{36}$$

Simplify.

$$x+6=6 x+6=-6$$

Subtract 6 from both sides of the equation.

$$x=0 x=-12$$