0=3t^2+14t+15

Solution for 0=3t^2+14t+15 equation:

Simplifying
0 = 3t2 + 14t + 15

Reorder the terms:
0 = 15 + 14t + 3t2

Solving
0 = 15 + 14t + 3t2

Solving for variable 't'.

Combine like terms: 0 + -15 = -15
-15 + -14t + -3t2 = 15 + 14t + 3t2 + -15 + -14t + -3t2

Reorder the terms:
-15 + -14t + -3t2 = 15 + -15 + 14t + -14t + 3t2 + -3t2

Combine like terms: 15 + -15 = 0
-15 + -14t + -3t2 = 0 + 14t + -14t + 3t2 + -3t2
-15 + -14t + -3t2 = 14t + -14t + 3t2 + -3t2

Combine like terms: 14t + -14t = 0
-15 + -14t + -3t2 = 0 + 3t2 + -3t2
-15 + -14t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
-15 + -14t + -3t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 14t + 3t2) = 0

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

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

Simplifying
3 + t = 0

Solving
3 + t = 0

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

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

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

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

Simplifying
t = -3
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 = {-3, -1.666666667}