-6b(-5+2b)+4(6b+8)=

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Solution for -6b(-5+2b)+4(6b+8)= equation: 


Simplifying
-6b(-5 + 2b) + 4(6b + 8) = 0
(-5 * -6b + 2b * -6b) + 4(6b + 8) = 0
(30b + -12b2) + 4(6b + 8) = 0

Reorder the terms:
30b + -12b2 + 4(8 + 6b) = 0
30b + -12b2 + (8 * 4 + 6b * 4) = 0
30b + -12b2 + (32 + 24b) = 0

Reorder the terms:
32 + 30b + 24b + -12b2 = 0

Combine like terms: 30b + 24b = 54b
32 + 54b + -12b2 = 0

Solving
32 + 54b + -12b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 27b + -6b2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + 27b + -6b2)' equal to zero and attempt to solve:

Simplifying
16 + 27b + -6b2 = 0

Solving
16 + 27b + -6b2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-2.666666667 + -4.5b + b2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -4.5b + 2.666666667 + b2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -4.5b + b2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -4.5b + b2 = 0 + 2.666666667
-4.5b + b2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-4.5b + b2 = 2.666666667

The b term is -4.5b.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5b + 5.0625 + b2 = 2.666666667 + 5.0625

Reorder the terms:
5.0625 + -4.5b + b2 = 2.666666667 + 5.0625

Combine like terms: 2.666666667 + 5.0625 = 7.729166667
5.0625 + -4.5b + b2 = 7.729166667

Factor a perfect square on the left side:
(b + -2.25)(b + -2.25) = 7.729166667

Calculate the square root of the right side: 2.780137886

Break this problem into two subproblems by setting 
(b + -2.25) equal to 2.780137886 and -2.780137886.


Subproblem 1
b + -2.25 = 2.780137886

Simplifying
b + -2.25 = 2.780137886

Reorder the terms:
-2.25 + b = 2.780137886

Solving
-2.25 + b = 2.780137886

Solving for variable 'b'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + b = 2.780137886 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + b = 2.780137886 + 2.25
b = 2.780137886 + 2.25

Combine like terms: 2.780137886 + 2.25 = 5.030137886
b = 5.030137886

Simplifying
b = 5.030137886


Subproblem 2
b + -2.25 = -2.780137886

Simplifying
b + -2.25 = -2.780137886

Reorder the terms:
-2.25 + b = -2.780137886

Solving
-2.25 + b = -2.780137886

Solving for variable 'b'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + b = -2.780137886 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + b = -2.780137886 + 2.25
b = -2.780137886 + 2.25

Combine like terms: -2.780137886 + 2.25 = -0.530137886
b = -0.530137886

Simplifying
b = -0.530137886


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {5.030137886, -0.530137886}
Solution
b = {5.030137886, -0.530137886}

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