4b(5b^2+b+6)=

Solution for 4b(5b^2+b+6)= equation:

Simplifying
4b(5b2 + b + 6) = 0

Reorder the terms:
4b(6 + b + 5b2) = 0
(6 * 4b + b * 4b + 5b2 * 4b) = 0
(24b + 4b2 + 20b3) = 0

Solving
24b + 4b2 + 20b3 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '4b'.
4b(6 + b + 5b2) = 0

Ignore the factor 4.
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 '(6 + b + 5b2)' equal to zero and attempt to solve:

Simplifying
6 + b + 5b2 = 0

Solving
6 + b + 5b2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
1.2 + 0.2b + b2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 0.2b + -1.2 + b2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 0.2b + b2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 0.2b + b2 = 0 + -1.2
0.2b + b2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
0.2b + b2 = -1.2

The b term is b.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.2b + 0.25 + b2 = -1.2 + 0.25

Reorder the terms:
0.25 + 0.2b + b2 = -1.2 + 0.25

Combine like terms: -1.2 + 0.25 = -0.95
0.25 + 0.2b + b2 = -0.95

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = -0.95

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
b = {0}