-15t^2+135t-270=0

Solution for -15t^2+135t-270=0 equation:

Simplifying
-15t2 + 135t + -270 = 0

Reorder the terms:
-270 + 135t + -15t2 = 0

Solving
-270 + 135t + -15t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-18 + 9t + -1t2) = 0

Factor a trinomial.
15((-6 + t)(3 + -1t)) = 0

Ignore the factor 15.
Subproblem 1
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
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 = {6, 3}