108=-36t^2+144t

Solution for 108=-36t^2+144t equation:

Simplifying
108 = -36t2 + 144t

Reorder the terms:
108 = 144t + -36t2

Solving
108 = 144t + -36t2

Solving for variable 't'.

Reorder the terms:
108 + -144t + 36t2 = 144t + -144t + -36t2 + 36t2

Combine like terms: 144t + -144t = 0
108 + -144t + 36t2 = 0 + -36t2 + 36t2
108 + -144t + 36t2 = -36t2 + 36t2

Combine like terms: -36t2 + 36t2 = 0
108 + -144t + 36t2 = 0

Factor out the Greatest Common Factor (GCF), '36'.
36(3 + -4t + t2) = 0

Factor a trinomial.
36((1 + -1t)(3 + -1t)) = 0

Ignore the factor 36.
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 '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {1, 3}