q(2q-1)(2q+1)=

Solution for q(2q-1)(2q+1)= equation:

Simplifying
q(2q + -1)(2q + 1) = 0

Reorder the terms:
q(-1 + 2q)(2q + 1) = 0

Reorder the terms:
q(-1 + 2q)(1 + 2q) = 0

Multiply (-1 + 2q) * (1 + 2q)
q(-1(1 + 2q) + 2q * (1 + 2q)) = 0
q((1 * -1 + 2q * -1) + 2q * (1 + 2q)) = 0
q((-1 + -2q) + 2q * (1 + 2q)) = 0
q(-1 + -2q + (1 * 2q + 2q * 2q)) = 0
q(-1 + -2q + (2q + 4q2)) = 0

Combine like terms: -2q + 2q = 0
q(-1 + 0 + 4q2) = 0
q(-1 + 4q2) = 0
(-1 * q + 4q2 * q) = 0
(-1q + 4q3) = 0

Solving
-1q + 4q3 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), 'q'.
q(-1 + 4q2) = 0

Factor a difference between two squares.
q((1 + 2q)(-1 + 2q)) = 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 '(1 + 2q)' equal to zero and attempt to solve:

Simplifying
1 + 2q = 0

Solving
1 + 2q = 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 + 2q = 0 + -1

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

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

Divide each side by '2'.
q = -0.5

Simplifying
q = -0.5
Subproblem 3
Set the factor '(-1 + 2q)' equal to zero and attempt to solve:

Simplifying
-1 + 2q = 0

Solving
-1 + 2q = 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 + 2q = 0 + 1

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

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

Divide each side by '2'.
q = 0.5

Simplifying
q = 0.5
Solution
q = {0, -0.5, 0.5}