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

$3 x^{2} = - 4 x$

Add $4 x$ to both sides of the equation.

$3 x^{2} + 4 x = 0$

Factor $x$ out of $3 x^{2} + 4 x$ .

Factor $x$ out of $3 x^{2}$ .

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

Factor $x$ out of $4 x$ .

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

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

$x (3 x + 4) = 0$

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

$x = 0$

$3 x + 4 = 0$

Set $x$ equal to $0$ .

$x = 0$

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

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

$3 x + 4 = 0$

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

Subtract $4$ from both sides of the equation.

$3 x = - 4$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

$x = 0, - \frac{4}{3}$