15b^2+65b-45=5

Solution for 15b^2+65b-45=5 equation:

Simplifying
15b2 + 65b + -45 = 5

Reorder the terms:
-45 + 65b + 15b2 = 5

Solving
-45 + 65b + 15b2 = 5

Solving for variable 'b'.

Reorder the terms:
-45 + -5 + 65b + 15b2 = 5 + -5

Combine like terms: -45 + -5 = -50
-50 + 65b + 15b2 = 5 + -5

Combine like terms: 5 + -5 = 0
-50 + 65b + 15b2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-10 + 13b + 3b2) = 0

Factor a trinomial.
5((-5 + -1b)(2 + -3b)) = 0

Ignore the factor 5.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + -3b)' equal to zero and attempt to solve:

Simplifying
2 + -3b = 0

Solving
2 + -3b = 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 + -3b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3b = 0 + -2
-3b = 0 + -2

Combine like terms: 0 + -2 = -2
-3b = -2

Divide each side by '-3'.
b = 0.6666666667

Simplifying
b = 0.6666666667
Solution
b = {-5, 0.6666666667}