q^3-4q^2+6q=0

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

Simplifying
q3 + -4q2 + 6q = 0

Reorder the terms:
6q + -4q2 + q3 = 0

Solving
6q + -4q2 + q3 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), 'q'.
q(6 + -4q + q2) = 0

Subproblem 1
Set the factor 'q' equal to zero and attempt to solve:

Simplifying
q = 0

Solving
q = 0

Move all terms containing q to the left, all other terms to the right.

Simplifying
q = 0
Subproblem 2
Set the factor '(6 + -4q + q2)' equal to zero and attempt to solve:

Simplifying
6 + -4q + q2 = 0

Solving
6 + -4q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -4q + -6 + q2 = 0 + -6

Reorder the terms:
6 + -6 + -4q + q2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -4q + q2 = 0 + -6
-4q + q2 = 0 + -6

Combine like terms: 0 + -6 = -6
-4q + q2 = -6

The q term is -4q.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4q + 4 + q2 = -6 + 4

Reorder the terms:
4 + -4q + q2 = -6 + 4

Combine like terms: -6 + 4 = -2
4 + -4q + q2 = -2

Factor a perfect square on the left side:
(q + -2)(q + -2) = -2

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
q = {0}