4t^3-18t^2+24t=0

Solution for 4t^3-18t^2+24t=0 equation:

Simplifying
4t3 + -18t2 + 24t = 0

Reorder the terms:
24t + -18t2 + 4t3 = 0

Solving
24t + -18t2 + 4t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2t'.
2t(12 + -9t + 2t2) = 0

Ignore the factor 2.
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 '(12 + -9t + 2t2)' equal to zero and attempt to solve:

Simplifying
12 + -9t + 2t2 = 0

Solving
12 + -9t + 2t2 = 0

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

Divide each side by '2'.
6 + -4.5t + t2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -4.5t + -6 + t2 = 0 + -6

Reorder the terms:
6 + -6 + -4.5t + t2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -4.5t + t2 = 0 + -6
-4.5t + t2 = 0 + -6

Combine like terms: 0 + -6 = -6
-4.5t + t2 = -6

The t term is -4.5t.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5t + 5.0625 + t2 = -6 + 5.0625

Reorder the terms:
5.0625 + -4.5t + t2 = -6 + 5.0625

Combine like terms: -6 + 5.0625 = -0.9375
5.0625 + -4.5t + t2 = -0.9375

Factor a perfect square on the left side:
(t + -2.25)(t + -2.25) = -0.9375

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}