t(3t+2)=0

Solution for t(3t+2)=0 equation:

Simplifying
t(3t + 2) = 0

Reorder the terms:
t(2 + 3t) = 0
(2 * t + 3t * t) = 0
(2t + 3t2) = 0

Solving
2t + 3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(2 + 3t) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

Move all terms containing t to the left, all other terms to the right.

Simplifying
t = 0
Subproblem 2
Set the factor '(2 + 3t)' equal to zero and attempt to solve:

Simplifying
2 + 3t = 0

Solving
2 + 3t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + 3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3t = 0 + -2
3t = 0 + -2

Combine like terms: 0 + -2 = -2
3t = -2

Divide each side by '3'.
t = -0.6666666667

Simplifying
t = -0.6666666667
Solution
t = {0, -0.6666666667}