Find the Roots (Zeros) (2x+4)(3x-2)=0

$(2 x + 4) (3 x - 2) = 0$

Step 1

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

$2 x + 4 = 0$

$3 x - 2 = 0$

Step 2

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

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

$2 x + 4 = 0$

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

Subtract $4$ from both sides of the equation.

$2 x = - 4$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $2$ .

$x = - 2$

Step 3

Set $3 x - 2$ equal to $0$ and solve for $x$ .

Set $3 x - 2$ equal to $0$ .

$3 x - 2 = 0$

Solve $3 x - 2 = 0$ for $x$ .

Add $2$ to both sides of the equation.

$3 x = 2$

Divide each term in $3 x = 2$ by $3$ and simplify.

Divide each term in $3 x = 2$ by $3$ .

$\frac{3 x}{3} = \frac{2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{2}{3}$

Divide $x$ by $1$ .

$x = \frac{2}{3}$

Step 4

The final solution is all the values that make $(2 x + 4) (3 x - 2) = 0$ true.

$x = - 2, \frac{2}{3}$

Step 5