-15(t^2+120t+10)=

Solution for -15(t^2+120t+10)= equation:

Simplifying
-15(t2 + 120t + 10) = 0

Reorder the terms:
-15(10 + 120t + t2) = 0
(10 * -15 + 120t * -15 + t2 * -15) = 0
(-150 + -1800t + -15t2) = 0

Solving
-150 + -1800t + -15t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-15'.
-15(10 + 120t + t2) = 0

Ignore the factor -15.
Subproblem 1
Set the factor '(10 + 120t + t2)' equal to zero and attempt to solve:

Simplifying
10 + 120t + t2 = 0

Solving
10 + 120t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 120t + -10 + t2 = 0 + -10

Reorder the terms:
10 + -10 + 120t + t2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 120t + t2 = 0 + -10
120t + t2 = 0 + -10

Combine like terms: 0 + -10 = -10
120t + t2 = -10

The t term is 120t.  Take half its coefficient (60).
Square it (3600) and add it to both sides.

Add '3600' to each side of the equation.
120t + 3600 + t2 = -10 + 3600

Reorder the terms:
3600 + 120t + t2 = -10 + 3600

Combine like terms: -10 + 3600 = 3590
3600 + 120t + t2 = 3590

Factor a perfect square on the left side:
(t + 60)(t + 60) = 3590

Calculate the square root of the right side: 59.916608716

Break this problem into two subproblems by setting 
(t + 60) equal to 59.916608716 and -59.916608716.

Subproblem 1
t + 60 = 59.916608716

Simplifying
t + 60 = 59.916608716

Reorder the terms:
60 + t = 59.916608716

Solving
60 + t = 59.916608716

Solving for variable 't'.

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

Add '-60' to each side of the equation.
60 + -60 + t = 59.916608716 + -60

Combine like terms: 60 + -60 = 0
0 + t = 59.916608716 + -60
t = 59.916608716 + -60

Combine like terms: 59.916608716 + -60 = -0.083391284
t = -0.083391284

Simplifying
t = -0.083391284

Subproblem 2
t + 60 = -59.916608716

Simplifying
t + 60 = -59.916608716

Reorder the terms:
60 + t = -59.916608716

Solving
60 + t = -59.916608716

Solving for variable 't'.

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

Add '-60' to each side of the equation.
60 + -60 + t = -59.916608716 + -60

Combine like terms: 60 + -60 = 0
0 + t = -59.916608716 + -60
t = -59.916608716 + -60

Combine like terms: -59.916608716 + -60 = -119.916608716
t = -119.916608716

Simplifying
t = -119.916608716

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.083391284, -119.916608716}
Solution
t = {-0.083391284, -119.916608716}