Find the Roots (Zeros) h(x)=(-4x-3)(x-3)

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

Step 1

Set $(- 4 x - 3) (x - 3)$ equal to $0$ .

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

Step 2

Solve for $x$ .

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

$- 4 x - 3 = 0$

$x - 3 = 0$

Set $- 4 x - 3$ equal to $0$ and solve for $x$ .

Set $- 4 x - 3$ equal to $0$ .

$- 4 x - 3 = 0$

Solve $- 4 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$- 4 x = 3$

Divide each term in $- 4 x = 3$ by $- 4$ and simplify.

Divide each term in $- 4 x = 3$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{3}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{3}{- 4}$

Divide $x$ by $1$ .

$x = \frac{3}{- 4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{4}$

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

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

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

$x = - \frac{3}{4}, 3$

Step 3