51=-12(b-3)11b

Solution for 51=-12(b-3)11b equation:

Simplifying
51 = -12(b + -3) * 11b

Reorder the terms:
51 = -12(-3 + b) * 11b

Reorder the terms for easier multiplication:
51 = -12 * 11b(-3 + b)

Multiply -12 * 11
51 = -132b(-3 + b)
51 = (-3 * -132b + b * -132b)
51 = (396b + -132b2)

Solving
51 = 396b + -132b2

Solving for variable 'b'.

Reorder the terms:
51 + -396b + 132b2 = 396b + -396b + -132b2 + 132b2

Combine like terms: 396b + -396b = 0
51 + -396b + 132b2 = 0 + -132b2 + 132b2
51 + -396b + 132b2 = -132b2 + 132b2

Combine like terms: -132b2 + 132b2 = 0
51 + -396b + 132b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(17 + -132b + 44b2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(17 + -132b + 44b2)' equal to zero and attempt to solve:

Simplifying
17 + -132b + 44b2 = 0

Solving
17 + -132b + 44b2 = 0

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

Divide each side by '44'.
0.3863636364 + -3b + b2 = 0

Move the constant term to the right:

Add '-0.3863636364' to each side of the equation.
0.3863636364 + -3b + -0.3863636364 + b2 = 0 + -0.3863636364

Reorder the terms:
0.3863636364 + -0.3863636364 + -3b + b2 = 0 + -0.3863636364

Combine like terms: 0.3863636364 + -0.3863636364 = 0.0000000000
0.0000000000 + -3b + b2 = 0 + -0.3863636364
-3b + b2 = 0 + -0.3863636364

Combine like terms: 0 + -0.3863636364 = -0.3863636364
-3b + b2 = -0.3863636364

The b term is -3b.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3b + 2.25 + b2 = -0.3863636364 + 2.25

Reorder the terms:
2.25 + -3b + b2 = -0.3863636364 + 2.25

Combine like terms: -0.3863636364 + 2.25 = 1.8636363636
2.25 + -3b + b2 = 1.8636363636

Factor a perfect square on the left side:
(b + -1.5)(b + -1.5) = 1.8636363636

Calculate the square root of the right side: 1.365150674

Break this problem into two subproblems by setting 
(b + -1.5) equal to 1.365150674 and -1.365150674.

Subproblem 1
b + -1.5 = 1.365150674

Simplifying
b + -1.5 = 1.365150674

Reorder the terms:
-1.5 + b = 1.365150674

Solving
-1.5 + b = 1.365150674

Solving for variable 'b'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + b = 1.365150674 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + b = 1.365150674 + 1.5
b = 1.365150674 + 1.5

Combine like terms: 1.365150674 + 1.5 = 2.865150674
b = 2.865150674

Simplifying
b = 2.865150674

Subproblem 2
b + -1.5 = -1.365150674

Simplifying
b + -1.5 = -1.365150674

Reorder the terms:
-1.5 + b = -1.365150674

Solving
-1.5 + b = -1.365150674

Solving for variable 'b'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + b = -1.365150674 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + b = -1.365150674 + 1.5
b = -1.365150674 + 1.5

Combine like terms: -1.365150674 + 1.5 = 0.134849326
b = 0.134849326

Simplifying
b = 0.134849326

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {2.865150674, 0.134849326}
Solution
b = {2.865150674, 0.134849326}