-5t^2+15t+150=0

Solution for -5t^2+15t+150=0 equation:

Simplifying
-5t2 + 15t + 150 = 0

Reorder the terms:
150 + 15t + -5t2 = 0

Solving
150 + 15t + -5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(30 + 3t + -1t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(30 + 3t + -1t2)' equal to zero and attempt to solve:

Simplifying
30 + 3t + -1t2 = 0

Solving
30 + 3t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-30 + -3t + t2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -3t + 30 + t2 = 0 + 30

Reorder the terms:
-30 + 30 + -3t + t2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -3t + t2 = 0 + 30
-3t + t2 = 0 + 30

Combine like terms: 0 + 30 = 30
-3t + t2 = 30

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = 30 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 30 + 2.25

Combine like terms: 30 + 2.25 = 32.25
2.25 + -3t + t2 = 32.25

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(t + -1.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
t + -1.5 = 5.678908346

Simplifying
t + -1.5 = 5.678908346

Reorder the terms:
-1.5 + t = 5.678908346

Solving
-1.5 + t = 5.678908346

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 5.678908346 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 5.678908346 + 1.5
t = 5.678908346 + 1.5

Combine like terms: 5.678908346 + 1.5 = 7.178908346
t = 7.178908346

Simplifying
t = 7.178908346

Subproblem 2
t + -1.5 = -5.678908346

Simplifying
t + -1.5 = -5.678908346

Reorder the terms:
-1.5 + t = -5.678908346

Solving
-1.5 + t = -5.678908346

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -5.678908346 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -5.678908346 + 1.5
t = -5.678908346 + 1.5

Combine like terms: -5.678908346 + 1.5 = -4.178908346
t = -4.178908346

Simplifying
t = -4.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.178908346, -4.178908346}
Solution
t = {7.178908346, -4.178908346}