2q^5-2q^4-4q^3=0

Solution for 2q^5-2q^4-4q^3=0 equation:

Simplifying
2q5 + -2q4 + -4q3 = 0

Reorder the terms:
-4q3 + -2q4 + 2q5 = 0

Solving
-4q3 + -2q4 + 2q5 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2q3'.
2q3(-2 + -1q + q2) = 0

Factor a trinomial.
2q3((-1 + -1q)(2 + -1q)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'q3' equal to zero and attempt to solve:

Simplifying
q3 = 0

Solving
q3 = 0

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

Simplifying
q3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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 '(2 + -1q)' equal to zero and attempt to solve:

Simplifying
2 + -1q = 0

Solving
2 + -1q = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1q = 0 + -2
-1q = 0 + -2

Combine like terms: 0 + -2 = -2
-1q = -2

Divide each side by '-1'.
q = 2

Simplifying
q = 2
Solution
q = {-1, 2}