2t^3-3t^2+108t=0

Solution for 2t^3-3t^2+108t=0 equation:

Simplifying
2t3 + -3t2 + 108t = 0

Reorder the terms:
108t + -3t2 + 2t3 = 0

Solving
108t + -3t2 + 2t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(108 + -3t + 2t2) = 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 '(108 + -3t + 2t2)' equal to zero and attempt to solve:

Simplifying
108 + -3t + 2t2 = 0

Solving
108 + -3t + 2t2 = 0

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

Divide each side by '2'.
54 + -1.5t + t2 = 0

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + -1.5t + -54 + t2 = 0 + -54

Reorder the terms:
54 + -54 + -1.5t + t2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -1.5t + t2 = 0 + -54
-1.5t + t2 = 0 + -54

Combine like terms: 0 + -54 = -54
-1.5t + t2 = -54

The t term is -1.5t.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5t + 0.5625 + t2 = -54 + 0.5625

Reorder the terms:
0.5625 + -1.5t + t2 = -54 + 0.5625

Combine like terms: -54 + 0.5625 = -53.4375
0.5625 + -1.5t + t2 = -53.4375

Factor a perfect square on the left side:
(t + -0.75)(t + -0.75) = -53.4375

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}