-15t^2+60t+10=0

Solution for -15t^2+60t+10=0 equation:

Simplifying
-15t2 + 60t + 10 = 0

Reorder the terms:
10 + 60t + -15t2 = 0

Solving
10 + 60t + -15t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + 12t + -3t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(2 + 12t + -3t2)' equal to zero and attempt to solve:

Simplifying
2 + 12t + -3t2 = 0

Solving
2 + 12t + -3t2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-0.6666666667 + -4t + t2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -4t + 0.6666666667 + t2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -4t + t2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -4t + t2 = 0 + 0.6666666667
-4t + t2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-4t + t2 = 0.6666666667

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = 0.6666666667 + 4

Reorder the terms:
4 + -4t + t2 = 0.6666666667 + 4

Combine like terms: 0.6666666667 + 4 = 4.6666666667
4 + -4t + t2 = 4.6666666667

Factor a perfect square on the left side:
(t + -2)(t + -2) = 4.6666666667

Calculate the square root of the right side: 2.160246899

Break this problem into two subproblems by setting 
(t + -2) equal to 2.160246899 and -2.160246899.

Subproblem 1
t + -2 = 2.160246899

Simplifying
t + -2 = 2.160246899

Reorder the terms:
-2 + t = 2.160246899

Solving
-2 + t = 2.160246899

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = 2.160246899 + 2

Combine like terms: -2 + 2 = 0
0 + t = 2.160246899 + 2
t = 2.160246899 + 2

Combine like terms: 2.160246899 + 2 = 4.160246899
t = 4.160246899

Simplifying
t = 4.160246899

Subproblem 2
t + -2 = -2.160246899

Simplifying
t + -2 = -2.160246899

Reorder the terms:
-2 + t = -2.160246899

Solving
-2 + t = -2.160246899

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = -2.160246899 + 2

Combine like terms: -2 + 2 = 0
0 + t = -2.160246899 + 2
t = -2.160246899 + 2

Combine like terms: -2.160246899 + 2 = -0.160246899
t = -0.160246899

Simplifying
t = -0.160246899

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.160246899, -0.160246899}
Solution
t = {4.160246899, -0.160246899}