4b^2+b=0

Solution for 4b^2+b=0 equation:

Simplifying
4b2 + b = 0

Reorder the terms:
b + 4b2 = 0

Solving
b + 4b2 = 0

Solving for variable 'b'.

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

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

Simplifying
b = 0

Solving
b = 0

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

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

Simplifying
1 + 4b = 0

Solving
1 + 4b = 0

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

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

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

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

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

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