b(b^2-12b+1)=0

Solution for b(b^2-12b+1)=0 equation:

Simplifying
b(b2 + -12b + 1) = 0

Reorder the terms:
b(1 + -12b + b2) = 0
(1 * b + -12b * b + b2 * b) = 0
(1b + -12b2 + b3) = 0

Solving
1b + -12b2 + b3 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), 'b'.
b(1 + -12b + b2) = 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 + -12b + b2)' equal to zero and attempt to solve:

Simplifying
1 + -12b + b2 = 0

Solving
1 + -12b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -12b + -1 + b2 = 0 + -1

Reorder the terms:
1 + -1 + -12b + b2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -12b + b2 = 0 + -1
-12b + b2 = 0 + -1

Combine like terms: 0 + -1 = -1
-12b + b2 = -1

The b term is -12b.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12b + 36 + b2 = -1 + 36

Reorder the terms:
36 + -12b + b2 = -1 + 36

Combine like terms: -1 + 36 = 35
36 + -12b + b2 = 35

Factor a perfect square on the left side:
(b + -6)(b + -6) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(b + -6) equal to 5.916079783 and -5.916079783.

Subproblem 1
b + -6 = 5.916079783

Simplifying
b + -6 = 5.916079783

Reorder the terms:
-6 + b = 5.916079783

Solving
-6 + b = 5.916079783

Solving for variable 'b'.

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

Add '6' to each side of the equation.
-6 + 6 + b = 5.916079783 + 6

Combine like terms: -6 + 6 = 0
0 + b = 5.916079783 + 6
b = 5.916079783 + 6

Combine like terms: 5.916079783 + 6 = 11.916079783
b = 11.916079783

Simplifying
b = 11.916079783

Subproblem 2
b + -6 = -5.916079783

Simplifying
b + -6 = -5.916079783

Reorder the terms:
-6 + b = -5.916079783

Solving
-6 + b = -5.916079783

Solving for variable 'b'.

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

Add '6' to each side of the equation.
-6 + 6 + b = -5.916079783 + 6

Combine like terms: -6 + 6 = 0
0 + b = -5.916079783 + 6
b = -5.916079783 + 6

Combine like terms: -5.916079783 + 6 = 0.083920217
b = 0.083920217

Simplifying
b = 0.083920217

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {11.916079783, 0.083920217}
Solution
b = {0, 11.916079783, 0.083920217}