6t^2+21t+15=0

Solution for 6t^2+21t+15=0 equation:

Simplifying
6t2 + 21t + 15 = 0

Reorder the terms:
15 + 21t + 6t2 = 0

Solving
15 + 21t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 7t + 2t2) = 0

Factor a trinomial.
3((5 + 2t)(1 + t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + 2t)' equal to zero and attempt to solve:

Simplifying
5 + 2t = 0

Solving
5 + 2t = 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 + 2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2t = 0 + -5
2t = 0 + -5

Combine like terms: 0 + -5 = -5
2t = -5

Divide each side by '2'.
t = -2.5

Simplifying
t = -2.5
Subproblem 2
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
Solution
t = {-2.5, -1}