2b(b-8)=30

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Solution for 2b(b-8)=30 equation: 


Simplifying
2b(b + -8) = 30

Reorder the terms:
2b(-8 + b) = 30
(-8 * 2b + b * 2b) = 30
(-16b + 2b2) = 30

Solving
-16b + 2b2 = 30

Solving for variable 'b'.

Reorder the terms:
-30 + -16b + 2b2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -16b + 2b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -8b + b2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + -8b + b2)' equal to zero and attempt to solve:

Simplifying
-15 + -8b + b2 = 0

Solving
-15 + -8b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -8b + 15 + b2 = 0 + 15

Reorder the terms:
-15 + 15 + -8b + b2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -8b + b2 = 0 + 15
-8b + b2 = 0 + 15

Combine like terms: 0 + 15 = 15
-8b + b2 = 15

The b term is -8b.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8b + 16 + b2 = 15 + 16

Reorder the terms:
16 + -8b + b2 = 15 + 16

Combine like terms: 15 + 16 = 31
16 + -8b + b2 = 31

Factor a perfect square on the left side:
(b + -4)(b + -4) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(b + -4) equal to 5.567764363 and -5.567764363.


Subproblem 1
b + -4 = 5.567764363

Simplifying
b + -4 = 5.567764363

Reorder the terms:
-4 + b = 5.567764363

Solving
-4 + b = 5.567764363

Solving for variable 'b'.

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

Add '4' to each side of the equation.
-4 + 4 + b = 5.567764363 + 4

Combine like terms: -4 + 4 = 0
0 + b = 5.567764363 + 4
b = 5.567764363 + 4

Combine like terms: 5.567764363 + 4 = 9.567764363
b = 9.567764363

Simplifying
b = 9.567764363


Subproblem 2
b + -4 = -5.567764363

Simplifying
b + -4 = -5.567764363

Reorder the terms:
-4 + b = -5.567764363

Solving
-4 + b = -5.567764363

Solving for variable 'b'.

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

Add '4' to each side of the equation.
-4 + 4 + b = -5.567764363 + 4

Combine like terms: -4 + 4 = 0
0 + b = -5.567764363 + 4
b = -5.567764363 + 4

Combine like terms: -5.567764363 + 4 = -1.567764363
b = -1.567764363

Simplifying
b = -1.567764363


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {9.567764363, -1.567764363}
Solution
b = {9.567764363, -1.567764363}

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