Solve -4x(x-6)=0

$$- 4 x ( x - 6 ) = 0$$

Solve for x

$$x=6$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply -4x by x-6.

$$-4x^{2}+24x=0$$

Factor out x.

$$x\left(-4x+24\right)=0$$

To find equation solutions, solve x=0 and -4x+24=0.

$$x=0 x=6$$

Steps Using the Quadratic Formula

Use the distributive property to multiply -4x by x-6.

$$-4x^{2}+24x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 24 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-24±\sqrt{24^{2}}}{2\left(-4\right)}$$

Take the square root of 24^{2}.

$$x=\frac{-24±24}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{-24±24}{-8}$$

Now solve the equation x=\frac{-24±24}{-8} when ± is plus. Add -24 to 24.

$$x=\frac{0}{-8}$$

Divide 0 by -8.

$$x=0$$

Now solve the equation x=\frac{-24±24}{-8} when ± is minus. Subtract 24 from -24.

$$x=-\frac{48}{-8}$$

Divide -48 by -8.

$$x=6$$

The equation is now solved.

$$x=0 x=6$$

Steps for Completing the Square

Use the distributive property to multiply -4x by x-6.

$$-4x^{2}+24x=0$$

Divide both sides by -4.

$$\frac{-4x^{2}+24x}{-4}=\frac{0}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$x^{2}+\frac{24}{-4}x=\frac{0}{-4}$$

Divide 24 by -4.

$$x^{2}-6x=\frac{0}{-4}$$

Divide 0 by -4.

$$x^{2}-6x=0$$

Divide -6, the coefficient of the x term, by 2 to get -3. Then add the square of -3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Square -3.

$$x^{2}-6x+9=9$$

Factor x^{2}-6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-3\right)^{2}=9$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{9}$$

Simplify.

$$x-3=3 x-3=-3$$

Add 3 to both sides of the equation.

$$x=6 x=0$$