-3b(10b+10)+5(b+2)=

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Solution for -3b(10b+10)+5(b+2)= equation: 


Simplifying
-3b(10b + 10) + 5(b + 2) = 0

Reorder the terms:
-3b(10 + 10b) + 5(b + 2) = 0
(10 * -3b + 10b * -3b) + 5(b + 2) = 0
(-30b + -30b2) + 5(b + 2) = 0

Reorder the terms:
-30b + -30b2 + 5(2 + b) = 0
-30b + -30b2 + (2 * 5 + b * 5) = 0
-30b + -30b2 + (10 + 5b) = 0

Reorder the terms:
10 + -30b + 5b + -30b2 = 0

Combine like terms: -30b + 5b = -25b
10 + -25b + -30b2 = 0

Solving
10 + -25b + -30b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -5b + -6b2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(2 + -5b + -6b2)' equal to zero and attempt to solve:

Simplifying
2 + -5b + -6b2 = 0

Solving
2 + -5b + -6b2 = 0

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

Divide each side by '-6'.
-0.3333333333 + 0.8333333333b + b2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.8333333333b + 0.3333333333 + b2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.8333333333b + b2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.8333333333b + b2 = 0 + 0.3333333333
0.8333333333b + b2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.8333333333b + b2 = 0.3333333333

The b term is 0.8333333333b.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333b + 0.1736111111 + b2 = 0.3333333333 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333b + b2 = 0.3333333333 + 0.1736111111

Combine like terms: 0.3333333333 + 0.1736111111 = 0.5069444444
0.1736111111 + 0.8333333333b + b2 = 0.5069444444

Factor a perfect square on the left side:
(b + 0.4166666667)(b + 0.4166666667) = 0.5069444444

Calculate the square root of the right side: 0.712000312

Break this problem into two subproblems by setting 
(b + 0.4166666667) equal to 0.712000312 and -0.712000312.


Subproblem 1
b + 0.4166666667 = 0.712000312

Simplifying
b + 0.4166666667 = 0.712000312

Reorder the terms:
0.4166666667 + b = 0.712000312

Solving
0.4166666667 + b = 0.712000312

Solving for variable 'b'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + b = 0.712000312 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + b = 0.712000312 + -0.4166666667
b = 0.712000312 + -0.4166666667

Combine like terms: 0.712000312 + -0.4166666667 = 0.2953336453
b = 0.2953336453

Simplifying
b = 0.2953336453


Subproblem 2
b + 0.4166666667 = -0.712000312

Simplifying
b + 0.4166666667 = -0.712000312

Reorder the terms:
0.4166666667 + b = -0.712000312

Solving
0.4166666667 + b = -0.712000312

Solving for variable 'b'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + b = -0.712000312 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + b = -0.712000312 + -0.4166666667
b = -0.712000312 + -0.4166666667

Combine like terms: -0.712000312 + -0.4166666667 = -1.1286669787
b = -1.1286669787

Simplifying
b = -1.1286669787


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.2953336453, -1.1286669787}
Solution
b = {0.2953336453, -1.1286669787}

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