Solve 4x(x-3)=16x

$$4 x ( x - 3 ) = 16 x$$

Solve for x

$$x=7$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply 4x by x-3.

$$4x^{2}-12x=16x$$

Subtract 16x from both sides.

$$4x^{2}-12x-16x=0$$

Combine -12x and -16x to get -28x.

$$4x^{2}-28x=0$$

Factor out x.

$$x\left(4x-28\right)=0$$

To find equation solutions, solve x=0 and 4x-28=0.

$$x=0 x=7$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 4x by x-3.

$$4x^{2}-12x=16x$$

Subtract 16x from both sides.

$$4x^{2}-12x-16x=0$$

Combine -12x and -16x to get -28x.

$$4x^{2}-28x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, -28 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-28\right)±\sqrt{\left(-28\right)^{2}}}{2\times 4}$$

Take the square root of \left(-28\right)^{2}.

$$x=\frac{-\left(-28\right)±28}{2\times 4}$$

The opposite of -28 is 28.

$$x=\frac{28±28}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{28±28}{8}$$

Now solve the equation x=\frac{28±28}{8} when ± is plus. Add 28 to 28.

$$x=\frac{56}{8}$$

Divide 56 by 8.

$$x=7$$

Now solve the equation x=\frac{28±28}{8} when ± is minus. Subtract 28 from 28.

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

Divide 0 by 8.

$$x=0$$

The equation is now solved.

$$x=7 x=0$$

Steps for Completing the Square

Use the distributive property to multiply 4x by x-3.

$$4x^{2}-12x=16x$$

Subtract 16x from both sides.

$$4x^{2}-12x-16x=0$$

Combine -12x and -16x to get -28x.

$$4x^{2}-28x=0$$

Divide both sides by 4.

$$\frac{4x^{2}-28x}{4}=\frac{0}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\left(-\frac{28}{4}\right)x=\frac{0}{4}$$

Divide -28 by 4.

$$x^{2}-7x=\frac{0}{4}$$

Divide 0 by 4.

$$x^{2}-7x=0$$

Divide -7, the coefficient of the x term, by 2 to get -\frac{7}{2}. Then add the square of -\frac{7}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=\left(-\frac{7}{2}\right)^{2}$$

Square -\frac{7}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-7x+\frac{49}{4}=\frac{49}{4}$$

Factor x^{2}-7x+\frac{49}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Simplify.

$$x-\frac{7}{2}=\frac{7}{2} x-\frac{7}{2}=-\frac{7}{2}$$

Add \frac{7}{2} to both sides of the equation.

$$x=7 x=0$$