Find the Roots (Zeros) y=(4x^2+12x)/(x+7)

$y = \frac{4 x^{2} + 12 x}{x + 7}$

Step 1

Set $\frac{4 x^{2} + 12 x}{x + 7}$ equal to $0$ .

$\frac{4 x^{2} + 12 x}{x + 7} = 0$

Step 2

Solve for $x$ .

Set the numerator equal to zero.

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

Solve the equation for $x$ .

Factor $4 x$ out of $4 x^{2} + 12 x$ .

Factor $4 x$ out of $4 x^{2}$ .

$4 x (x) + 12 x = 0$

Factor $4 x$ out of $12 x$ .

$4 x (x) + 4 x (3) = 0$

Factor $4 x$ out of $4 x (x) + 4 x (3)$ .

$4 x (x + 3) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x + 3 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

The final solution is all the values that make $4 x (x + 3) = 0$ true.

$x = 0, - 3$

Step 3