-t^3+12t^2-45t=0

Solution for -t^3+12t^2-45t=0 equation:

Simplifying
-1t3 + 12t2 + -45t = 0

Reorder the terms:
-45t + 12t2 + -1t3 = 0

Solving
-45t + 12t2 + -1t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-45 + 12t + -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 '(-45 + 12t + -1t2)' equal to zero and attempt to solve:

Simplifying
-45 + 12t + -1t2 = 0

Solving
-45 + 12t + -1t2 = 0

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

Divide each side by '-1'.
45 + -12t + t2 = 0

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + -12t + -45 + t2 = 0 + -45

Reorder the terms:
45 + -45 + -12t + t2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -12t + t2 = 0 + -45
-12t + t2 = 0 + -45

Combine like terms: 0 + -45 = -45
-12t + t2 = -45

The t term is -12t.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12t + 36 + t2 = -45 + 36

Reorder the terms:
36 + -12t + t2 = -45 + 36

Combine like terms: -45 + 36 = -9
36 + -12t + t2 = -9

Factor a perfect square on the left side:
(t + -6)(t + -6) = -9

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}