108=18t^2+90t

Solution for 108=18t^2+90t equation:

Simplifying
108 = 18t2 + 90t

Reorder the terms:
108 = 90t + 18t2

Solving
108 = 90t + 18t2

Solving for variable 't'.

Reorder the terms:
108 + -90t + -18t2 = 90t + -90t + 18t2 + -18t2

Combine like terms: 90t + -90t = 0
108 + -90t + -18t2 = 0 + 18t2 + -18t2
108 + -90t + -18t2 = 18t2 + -18t2

Combine like terms: 18t2 + -18t2 = 0
108 + -90t + -18t2 = 0

Factor out the Greatest Common Factor (GCF), '18'.
18(6 + -5t + -1t2) = 0

Factor a trinomial.
18((1 + -1t)(6 + t)) = 0

Ignore the factor 18.
Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

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

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

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

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

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

Simplifying
6 + t = 0

Solving
6 + t = 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 + t = 0 + -6

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

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

Simplifying
t = -6
Solution
t = {1, -6}