-t^3+15t^2-72t=0

Solution for -t^3+15t^2-72t=0 equation:

Simplifying
-1t3 + 15t2 + -72t = 0

Reorder the terms:
-72t + 15t2 + -1t3 = 0

Solving
-72t + 15t2 + -1t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-72 + 15t + -1t2) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(-72 + 15t + -1t2)' equal to zero and attempt to solve:

Simplifying
-72 + 15t + -1t2 = 0

Solving
-72 + 15t + -1t2 = 0

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

Divide each side by '-1'.
72 + -15t + t2 = 0

Move the constant term to the right:

Add '-72' to each side of the equation.
72 + -15t + -72 + t2 = 0 + -72

Reorder the terms:
72 + -72 + -15t + t2 = 0 + -72

Combine like terms: 72 + -72 = 0
0 + -15t + t2 = 0 + -72
-15t + t2 = 0 + -72

Combine like terms: 0 + -72 = -72
-15t + t2 = -72

The t term is -15t.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15t + 56.25 + t2 = -72 + 56.25

Reorder the terms:
56.25 + -15t + t2 = -72 + 56.25

Combine like terms: -72 + 56.25 = -15.75
56.25 + -15t + t2 = -15.75

Factor a perfect square on the left side:
(t + -7.5)(t + -7.5) = -15.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
t = {0}