3t^2+5t+2=0

Solution for 3t^2+5t+2=0 equation:

Simplifying
3t2 + 5t + 2 = 0

Reorder the terms:
2 + 5t + 3t2 = 0

Solving
2 + 5t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(1 + t)(2 + 3t) = 0

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

Simplifying
1 + t = 0

Solving
1 + t = 0

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

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0 + -1
t = 0 + -1

Combine like terms: 0 + -1 = -1
t = -1

Simplifying
t = -1
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 = {-1, -0.6666666667}