Find the Roots (Zeros) (x-7)(-4x-2)=0

$(x - 7) (- 4 x - 2) = 0$

Step 1

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

$x - 7 = 0$

$- 4 x - 2 = 0$

Step 2

Set $x - 7$ equal to $0$ and solve for $x$ .

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

Step 3

Set $- 4 x - 2$ equal to $0$ and solve for $x$ .

Set $- 4 x - 2$ equal to $0$ .

$- 4 x - 2 = 0$

Solve $- 4 x - 2 = 0$ for $x$ .

Add $2$ to both sides of the equation.

$- 4 x = 2$

Divide each term in $- 4 x = 2$ by $- 4$ and simplify.

Divide each term in $- 4 x = 2$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{2}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{2}{- 4}$

Divide $x$ by $1$ .

$x = \frac{2}{- 4}$

Simplify the right side.

Cancel the common factor of $2$ and $- 4$ .

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$x = \frac{2 \cdot 1}{2 \cdot - 2}$

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot - 2}$

Rewrite the expression.

$x = \frac{1}{- 2}$

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

Step 4

The final solution is all the values that make $(x - 7) (- 4 x - 2) = 0$ true.

$x = 7, - \frac{1}{2}$

Step 5