0=-15t^2+120t-105

Solution for 0=-15t^2+120t-105 equation:

Simplifying
0 = -15t2 + 120t + -105

Reorder the terms:
0 = -105 + 120t + -15t2

Solving
0 = -105 + 120t + -15t2

Solving for variable 't'.

Combine like terms: 0 + 105 = 105
105 + -120t + 15t2 = -105 + 120t + -15t2 + 105 + -120t + 15t2

Reorder the terms:
105 + -120t + 15t2 = -105 + 105 + 120t + -120t + -15t2 + 15t2

Combine like terms: -105 + 105 = 0
105 + -120t + 15t2 = 0 + 120t + -120t + -15t2 + 15t2
105 + -120t + 15t2 = 120t + -120t + -15t2 + 15t2

Combine like terms: 120t + -120t = 0
105 + -120t + 15t2 = 0 + -15t2 + 15t2
105 + -120t + 15t2 = -15t2 + 15t2

Combine like terms: -15t2 + 15t2 = 0
105 + -120t + 15t2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(7 + -8t + t2) = 0

Factor a trinomial.
15((1 + -1t)(7 + -1t)) = 0

Ignore the factor 15.
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 '(7 + -1t)' equal to zero and attempt to solve:

Simplifying
7 + -1t = 0

Solving
7 + -1t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t = 0 + -7
-1t = 0 + -7

Combine like terms: 0 + -7 = -7
-1t = -7

Divide each side by '-1'.
t = 7

Simplifying
t = 7
Solution
t = {1, 7}