-15t^2+135t-280=0

Solution for -15t^2+135t-280=0 equation:

Simplifying
-15t2 + 135t + -280 = 0

Reorder the terms:
-280 + 135t + -15t2 = 0

Solving
-280 + 135t + -15t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-56 + 27t + -3t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-56 + 27t + -3t2)' equal to zero and attempt to solve:

Simplifying
-56 + 27t + -3t2 = 0

Solving
-56 + 27t + -3t2 = 0

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

Divide each side by '-3'.
18.66666667 + -9t + t2 = 0

Move the constant term to the right:

Add '-18.66666667' to each side of the equation.
18.66666667 + -9t + -18.66666667 + t2 = 0 + -18.66666667

Reorder the terms:
18.66666667 + -18.66666667 + -9t + t2 = 0 + -18.66666667

Combine like terms: 18.66666667 + -18.66666667 = 0.00000000
0.00000000 + -9t + t2 = 0 + -18.66666667
-9t + t2 = 0 + -18.66666667

Combine like terms: 0 + -18.66666667 = -18.66666667
-9t + t2 = -18.66666667

The t term is -9t.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9t + 20.25 + t2 = -18.66666667 + 20.25

Reorder the terms:
20.25 + -9t + t2 = -18.66666667 + 20.25

Combine like terms: -18.66666667 + 20.25 = 1.58333333
20.25 + -9t + t2 = 1.58333333

Factor a perfect square on the left side:
(t + -4.5)(t + -4.5) = 1.58333333

Calculate the square root of the right side: 1.258305738

Break this problem into two subproblems by setting 
(t + -4.5) equal to 1.258305738 and -1.258305738.

Subproblem 1
t + -4.5 = 1.258305738

Simplifying
t + -4.5 = 1.258305738

Reorder the terms:
-4.5 + t = 1.258305738

Solving
-4.5 + t = 1.258305738

Solving for variable 't'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + t = 1.258305738 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = 1.258305738 + 4.5
t = 1.258305738 + 4.5

Combine like terms: 1.258305738 + 4.5 = 5.758305738
t = 5.758305738

Simplifying
t = 5.758305738

Subproblem 2
t + -4.5 = -1.258305738

Simplifying
t + -4.5 = -1.258305738

Reorder the terms:
-4.5 + t = -1.258305738

Solving
-4.5 + t = -1.258305738

Solving for variable 't'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + t = -1.258305738 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = -1.258305738 + 4.5
t = -1.258305738 + 4.5

Combine like terms: -1.258305738 + 4.5 = 3.241694262
t = 3.241694262

Simplifying
t = 3.241694262

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.758305738, 3.241694262}
Solution
t = {5.758305738, 3.241694262}