-4t^3+9t^2-6t=0

Solution for -4t^3+9t^2-6t=0 equation:

Simplifying
-4t3 + 9t2 + -6t = 0

Reorder the terms:
-6t + 9t2 + -4t3 = 0

Solving
-6t + 9t2 + -4t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-6 + 9t + -4t2) = 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 '(-6 + 9t + -4t2)' equal to zero and attempt to solve:

Simplifying
-6 + 9t + -4t2 = 0

Solving
-6 + 9t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
1.5 + -2.25t + t2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -2.25t + -1.5 + t2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -2.25t + t2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -2.25t + t2 = 0 + -1.5
-2.25t + t2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-2.25t + t2 = -1.5

The t term is -2.25t.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25t + 1.265625 + t2 = -1.5 + 1.265625

Reorder the terms:
1.265625 + -2.25t + t2 = -1.5 + 1.265625

Combine like terms: -1.5 + 1.265625 = -0.234375
1.265625 + -2.25t + t2 = -0.234375

Factor a perfect square on the left side:
(t + -1.125)(t + -1.125) = -0.234375

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}