q(4q+1)=0

Solution for q(4q+1)=0 equation:

Simplifying
q(4q + 1) = 0

Reorder the terms:
q(1 + 4q) = 0
(1 * q + 4q * q) = 0
(1q + 4q2) = 0

Solving
1q + 4q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), 'q'.
q(1 + 4q) = 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 + 4q)' equal to zero and attempt to solve:

Simplifying
1 + 4q = 0

Solving
1 + 4q = 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 + 4q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4q = 0 + -1
4q = 0 + -1

Combine like terms: 0 + -1 = -1
4q = -1

Divide each side by '4'.
q = -0.25

Simplifying
q = -0.25
Solution
q = {0, -0.25}