175b^2+227b=-60+7b

Solution for 175b^2+227b=-60+7b equation:

Simplifying
175b2 + 227b = -60 + 7b

Reorder the terms:
227b + 175b2 = -60 + 7b

Solving
227b + 175b2 = -60 + 7b

Solving for variable 'b'.

Reorder the terms:
60 + 227b + -7b + 175b2 = -60 + 7b + 60 + -7b

Combine like terms: 227b + -7b = 220b
60 + 220b + 175b2 = -60 + 7b + 60 + -7b

Reorder the terms:
60 + 220b + 175b2 = -60 + 60 + 7b + -7b

Combine like terms: -60 + 60 = 0
60 + 220b + 175b2 = 0 + 7b + -7b
60 + 220b + 175b2 = 7b + -7b

Combine like terms: 7b + -7b = 0
60 + 220b + 175b2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(12 + 44b + 35b2) = 0

Factor a trinomial.
5((6 + 7b)(2 + 5b)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(6 + 7b)' equal to zero and attempt to solve:

Simplifying
6 + 7b = 0

Solving
6 + 7b = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7b = 0 + -6
7b = 0 + -6

Combine like terms: 0 + -6 = -6
7b = -6

Divide each side by '7'.
b = -0.8571428571

Simplifying
b = -0.8571428571
Subproblem 2
Set the factor '(2 + 5b)' equal to zero and attempt to solve:

Simplifying
2 + 5b = 0

Solving
2 + 5b = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5b = 0 + -2
5b = 0 + -2

Combine like terms: 0 + -2 = -2
5b = -2

Divide each side by '5'.
b = -0.4

Simplifying
b = -0.4
Solution
b = {-0.8571428571, -0.4}