15b^2-190b-80=0

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Solution for 15b^2-190b-80=0 equation: 


Simplifying
15b2 + -190b + -80 = 0

Reorder the terms:
-80 + -190b + 15b2 = 0

Solving
-80 + -190b + 15b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-16 + -38b + 3b2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-16 + -38b + 3b2)' equal to zero and attempt to solve:

Simplifying
-16 + -38b + 3b2 = 0

Solving
-16 + -38b + 3b2 = 0

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

Divide each side by '3'.
-5.333333333 + -12.66666667b + b2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -12.66666667b + 5.333333333 + b2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -12.66666667b + b2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -12.66666667b + b2 = 0 + 5.333333333
-12.66666667b + b2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-12.66666667b + b2 = 5.333333333

The b term is -12.66666667b.  Take half its coefficient (-6.333333335).
Square it (40.11111113) and add it to both sides.

Add '40.11111113' to each side of the equation.
-12.66666667b + 40.11111113 + b2 = 5.333333333 + 40.11111113

Reorder the terms:
40.11111113 + -12.66666667b + b2 = 5.333333333 + 40.11111113

Combine like terms: 5.333333333 + 40.11111113 = 45.444444463
40.11111113 + -12.66666667b + b2 = 45.444444463

Factor a perfect square on the left side:
(b + -6.333333335)(b + -6.333333335) = 45.444444463

Calculate the square root of the right side: 6.741249473

Break this problem into two subproblems by setting 
(b + -6.333333335) equal to 6.741249473 and -6.741249473.


Subproblem 1
b + -6.333333335 = 6.741249473

Simplifying
b + -6.333333335 = 6.741249473

Reorder the terms:
-6.333333335 + b = 6.741249473

Solving
-6.333333335 + b = 6.741249473

Solving for variable 'b'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + b = 6.741249473 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + b = 6.741249473 + 6.333333335
b = 6.741249473 + 6.333333335

Combine like terms: 6.741249473 + 6.333333335 = 13.074582808
b = 13.074582808

Simplifying
b = 13.074582808


Subproblem 2
b + -6.333333335 = -6.741249473

Simplifying
b + -6.333333335 = -6.741249473

Reorder the terms:
-6.333333335 + b = -6.741249473

Solving
-6.333333335 + b = -6.741249473

Solving for variable 'b'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + b = -6.741249473 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + b = -6.741249473 + 6.333333335
b = -6.741249473 + 6.333333335

Combine like terms: -6.741249473 + 6.333333335 = -0.407916138
b = -0.407916138

Simplifying
b = -0.407916138


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {13.074582808, -0.407916138}
Solution
b = {13.074582808, -0.407916138}

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