3t^2+3t-90=0

Solution for 3t^2+3t-90=0 equation:

Simplifying
3t2 + 3t + -90 = 0

Reorder the terms:
-90 + 3t + 3t2 = 0

Solving
-90 + 3t + 3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + t + t2) = 0

Factor a trinomial.
3((-6 + -1t)(5 + -1t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 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 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-6, 5}