6b^2-31b+75=-5+2b^2+5b

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Solution for 6b^2-31b+75=-5+2b^2+5b equation: 


Simplifying
6b2 + -31b + 75 = -5 + 2b2 + 5b

Reorder the terms:
75 + -31b + 6b2 = -5 + 2b2 + 5b

Reorder the terms:
75 + -31b + 6b2 = -5 + 5b + 2b2

Solving
75 + -31b + 6b2 = -5 + 5b + 2b2

Solving for variable 'b'.

Reorder the terms:
75 + 5 + -31b + -5b + 6b2 + -2b2 = -5 + 5b + 2b2 + 5 + -5b + -2b2

Combine like terms: 75 + 5 = 80
80 + -31b + -5b + 6b2 + -2b2 = -5 + 5b + 2b2 + 5 + -5b + -2b2

Combine like terms: -31b + -5b = -36b
80 + -36b + 6b2 + -2b2 = -5 + 5b + 2b2 + 5 + -5b + -2b2

Combine like terms: 6b2 + -2b2 = 4b2
80 + -36b + 4b2 = -5 + 5b + 2b2 + 5 + -5b + -2b2

Reorder the terms:
80 + -36b + 4b2 = -5 + 5 + 5b + -5b + 2b2 + -2b2

Combine like terms: -5 + 5 = 0
80 + -36b + 4b2 = 0 + 5b + -5b + 2b2 + -2b2
80 + -36b + 4b2 = 5b + -5b + 2b2 + -2b2

Combine like terms: 5b + -5b = 0
80 + -36b + 4b2 = 0 + 2b2 + -2b2
80 + -36b + 4b2 = 2b2 + -2b2

Combine like terms: 2b2 + -2b2 = 0
80 + -36b + 4b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + -9b + b2) = 0

Factor a trinomial.
4((4 + -1b)(5 + -1b)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(4 + -1b)' equal to zero and attempt to solve:

Simplifying
4 + -1b = 0

Solving
4 + -1b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1b = 0 + -4
-1b = 0 + -4

Combine like terms: 0 + -4 = -4
-1b = -4

Divide each side by '-1'.
b = 4

Simplifying
b = 4

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

Simplifying
5 + -1b = 0

Solving
5 + -1b = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Solution
b = {4, 5}

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