w(4w+1)=0

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

Simplifying
w(4w + 1) = 0

Reorder the terms:
w(1 + 4w) = 0
(1 * w + 4w * w) = 0
(1w + 4w2) = 0

Solving
1w + 4w2 = 0

Solving for variable 'w'.

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

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

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0
Subproblem 2
Set the factor '(1 + 4w)' equal to zero and attempt to solve:

Simplifying
1 + 4w = 0

Solving
1 + 4w = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4w = 0 + -1

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

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

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

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