5b^3(8b^2-1)=0

Solution for 5b^3(8b^2-1)=0 equation:

Simplifying
5b3(8b2 + -1) = 0

Reorder the terms:
5b3(-1 + 8b2) = 0
(-1 * 5b3 + 8b2 * 5b3) = 0
(-5b3 + 40b5) = 0

Solving
-5b3 + 40b5 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '5b3'.
5b3(-1 + 8b2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'b3' equal to zero and attempt to solve:

Simplifying
b3 = 0

Solving
b3 = 0

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

Simplifying
b3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-1 + 8b2)' equal to zero and attempt to solve:

Simplifying
-1 + 8b2 = 0

Solving
-1 + 8b2 = 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 + 8b2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 8b2 = 0 + 1
8b2 = 0 + 1

Combine like terms: 0 + 1 = 1
8b2 = 1

Divide each side by '8'.
b2 = 0.125

Simplifying
b2 = 0.125

Take the square root of each side:
b = {-0.353553391, 0.353553391}
Solution
b = {-0.353553391, 0.353553391}