T^3-3T^2+6T=0

Solution for T^3-3T^2+6T=0 equation:

Simplifying
T3 + -3T2 + 6T = 0

Reorder the terms:
6T + -3T2 + T3 = 0

Solving
6T + -3T2 + T3 = 0

Solving for variable 'T'.

Factor out the Greatest Common Factor (GCF), 'T'.
T(6 + -3T + T2) = 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 + -3T + T2)' equal to zero and attempt to solve:

Simplifying
6 + -3T + T2 = 0

Solving
6 + -3T + T2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -3T + -6 + T2 = 0 + -6

Reorder the terms:
6 + -6 + -3T + T2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -3T + T2 = 0 + -6
-3T + T2 = 0 + -6

Combine like terms: 0 + -6 = -6
-3T + T2 = -6

The T term is -3T.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3T + 2.25 + T2 = -6 + 2.25

Reorder the terms:
2.25 + -3T + T2 = -6 + 2.25

Combine like terms: -6 + 2.25 = -3.75
2.25 + -3T + T2 = -3.75

Factor a perfect square on the left side:
(T + -1.5)(T + -1.5) = -3.75

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}