6*q^3-16*q^2+10*q=0

Solution for 6*q^3-16*q^2+10*q=0 equation:

Simplifying
6q3 + -16q2 + 10q = 0

Reorder the terms:
10q + -16q2 + 6q3 = 0

Solving
10q + -16q2 + 6q3 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2q'.
2q(5 + -8q + 3q2) = 0

Factor a trinomial.
2q((1 + -1q)(5 + -3q)) = 0

Ignore the factor 2.
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 '(1 + -1q)' equal to zero and attempt to solve:

Simplifying
1 + -1q = 0

Solving
1 + -1q = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1q = 0 + -1
-1q = 0 + -1

Combine like terms: 0 + -1 = -1
-1q = -1

Divide each side by '-1'.
q = 1

Simplifying
q = 1
Subproblem 3
Set the factor '(5 + -3q)' equal to zero and attempt to solve:

Simplifying
5 + -3q = 0

Solving
5 + -3q = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3q = 0 + -5
-3q = 0 + -5

Combine like terms: 0 + -5 = -5
-3q = -5

Divide each side by '-3'.
q = 1.666666667

Simplifying
q = 1.666666667
Solution
q = {0, 1, 1.666666667}