0=-5t^2+15t+30

Solution for 0=-5t^2+15t+30 equation:

Simplifying
0 = -5t2 + 15t + 30

Reorder the terms:
0 = 30 + 15t + -5t2

Solving
0 = 30 + 15t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -30 = -30
-30 + -15t + 5t2 = 30 + 15t + -5t2 + -30 + -15t + 5t2

Reorder the terms:
-30 + -15t + 5t2 = 30 + -30 + 15t + -15t + -5t2 + 5t2

Combine like terms: 30 + -30 = 0
-30 + -15t + 5t2 = 0 + 15t + -15t + -5t2 + 5t2
-30 + -15t + 5t2 = 15t + -15t + -5t2 + 5t2

Combine like terms: 15t + -15t = 0
-30 + -15t + 5t2 = 0 + -5t2 + 5t2
-30 + -15t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-30 + -15t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + -3t + t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -3t + t2)' equal to zero and attempt to solve:

Simplifying
-6 + -3t + t2 = 0

Solving
-6 + -3t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -3t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + -3t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -3t + t2 = 0 + 6
-3t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
-3t + t2 = 6

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 = 6 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + -3t + t2 = 8.25

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(t + -1.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
t + -1.5 = 2.872281323

Simplifying
t + -1.5 = 2.872281323

Reorder the terms:
-1.5 + t = 2.872281323

Solving
-1.5 + t = 2.872281323

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 = 2.872281323 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 2.872281323 + 1.5
t = 2.872281323 + 1.5

Combine like terms: 2.872281323 + 1.5 = 4.372281323
t = 4.372281323

Simplifying
t = 4.372281323

Subproblem 2
t + -1.5 = -2.872281323

Simplifying
t + -1.5 = -2.872281323

Reorder the terms:
-1.5 + t = -2.872281323

Solving
-1.5 + t = -2.872281323

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 = -2.872281323 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -2.872281323 + 1.5
t = -2.872281323 + 1.5

Combine like terms: -2.872281323 + 1.5 = -1.372281323
t = -1.372281323

Simplifying
t = -1.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.372281323, -1.372281323}
Solution
t = {4.372281323, -1.372281323}