Solve for t t(3t+1)=0

$t (3 t + 1) = 0$

Step 1

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

$t = 0$

$3 t + 1 = 0$

Step 2

Set $t$ equal to $0$ .

$t = 0$

Step 3

Set $3 t + 1$ equal to $0$ and solve for $t$ .

Set $3 t + 1$ equal to $0$ .

$3 t + 1 = 0$

Solve $3 t + 1 = 0$ for $t$ .

Subtract $1$ from both sides of the equation.

$3 t = - 1$

Divide each term in $3 t = - 1$ by $3$ and simplify.

Divide each term in $3 t = - 1$ by $3$ .

$\frac{3 t}{3} = \frac{- 1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 t}{3} = \frac{- 1}{3}$

Divide $t$ by $1$ .

$t = \frac{- 1}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$t = - \frac{1}{3}$

Step 4

The final solution is all the values that make $t (3 t + 1) = 0$ true.

$t = 0, - \frac{1}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = 0, - \frac{1}{3}$

Decimal Form:

$t = 0, - 0.\overline{3}$