(b+10)(3b)=180

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Solution for (b+10)(3b)=180 equation: 


Simplifying
(b + 10)(3b) = 180

Reorder the terms:
(10 + b)(3b) = 180

Remove parenthesis around (3b)
(10 + b) * 3b = 180

Reorder the terms for easier multiplication:
3b(10 + b) = 180
(10 * 3b + b * 3b) = 180
(30b + 3b2) = 180

Solving
30b + 3b2 = 180

Solving for variable 'b'.

Reorder the terms:
-180 + 30b + 3b2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 30b + 3b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + 10b + b2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-60 + 10b + b2)' equal to zero and attempt to solve:

Simplifying
-60 + 10b + b2 = 0

Solving
-60 + 10b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 10b + 60 + b2 = 0 + 60

Reorder the terms:
-60 + 60 + 10b + b2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 10b + b2 = 0 + 60
10b + b2 = 0 + 60

Combine like terms: 0 + 60 = 60
10b + b2 = 60

The b term is 10b.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10b + 25 + b2 = 60 + 25

Reorder the terms:
25 + 10b + b2 = 60 + 25

Combine like terms: 60 + 25 = 85
25 + 10b + b2 = 85

Factor a perfect square on the left side:
(b + 5)(b + 5) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(b + 5) equal to 9.219544457 and -9.219544457.


Subproblem 1
b + 5 = 9.219544457

Simplifying
b + 5 = 9.219544457

Reorder the terms:
5 + b = 9.219544457

Solving
5 + b = 9.219544457

Solving for variable 'b'.

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

Add '-5' to each side of the equation.
5 + -5 + b = 9.219544457 + -5

Combine like terms: 5 + -5 = 0
0 + b = 9.219544457 + -5
b = 9.219544457 + -5

Combine like terms: 9.219544457 + -5 = 4.219544457
b = 4.219544457

Simplifying
b = 4.219544457


Subproblem 2
b + 5 = -9.219544457

Simplifying
b + 5 = -9.219544457

Reorder the terms:
5 + b = -9.219544457

Solving
5 + b = -9.219544457

Solving for variable 'b'.

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

Add '-5' to each side of the equation.
5 + -5 + b = -9.219544457 + -5

Combine like terms: 5 + -5 = 0
0 + b = -9.219544457 + -5
b = -9.219544457 + -5

Combine like terms: -9.219544457 + -5 = -14.219544457
b = -14.219544457

Simplifying
b = -14.219544457


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {4.219544457, -14.219544457}
Solution
b = {4.219544457, -14.219544457}

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