q(2q^2+q)=

Solution for q(2q^2+q)= equation:

Simplifying
q(2q2 + q) = 0

Reorder the terms:
q(q + 2q2) = 0
(q * q + 2q2 * q) = 0
(q2 + 2q3) = 0

Solving
q2 + 2q3 = 0

Solving for variable 'q'.

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

Subproblem 1
Set the factor 'q2' equal to zero and attempt to solve:

Simplifying
q2 = 0

Solving
q2 = 0

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

Simplifying
q2 = 0

Take the square root of each side:
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
Solution
q = {0, -0.5}