3t^2+11t+10=0

Solution for 3t^2+11t+10=0 equation:

Simplifying
3t2 + 11t + 10 = 0

Reorder the terms:
10 + 11t + 3t2 = 0

Solving
10 + 11t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(2 + t)(5 + 3t) = 0

Subproblem 1
Set the factor '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 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 + t = 0 + -2

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

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

Simplifying
t = -2
Subproblem 2
Set the factor '(5 + 3t)' equal to zero and attempt to solve:

Simplifying
5 + 3t = 0

Solving
5 + 3t = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3t = 0 + -5
3t = 0 + -5

Combine like terms: 0 + -5 = -5
3t = -5

Divide each side by '3'.
t = -1.666666667

Simplifying
t = -1.666666667
Solution
t = {-2, -1.666666667}