-15t^2+75t-90=0

Solution for -15t^2+75t-90=0 equation:

Simplifying
-15t2 + 75t + -90 = 0

Reorder the terms:
-90 + 75t + -15t2 = 0

Solving
-90 + 75t + -15t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-6 + 5t + -1t2) = 0

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

Ignore the factor 15.
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 '(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
Solution
t = {3, 2}