90=-15t^2+75t

Solution for 90=-15t^2+75t equation:

Simplifying
90 = -15t2 + 75t

Reorder the terms:
90 = 75t + -15t2

Solving
90 = 75t + -15t2

Solving for variable 't'.

Reorder the terms:
90 + -75t + 15t2 = 75t + -75t + -15t2 + 15t2

Combine like terms: 75t + -75t = 0
90 + -75t + 15t2 = 0 + -15t2 + 15t2
90 + -75t + 15t2 = -15t2 + 15t2

Combine like terms: -15t2 + 15t2 = 0
90 + -75t + 15t2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(6 + -5t + t2) = 0

Factor a trinomial.
15((2 + -1t)(3 + -1t)) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
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 = {2, 3}