15b^2-69b-126=0

Solution for 15b^2-69b-126=0 equation:

Simplifying
15b2 + -69b + -126 = 0

Reorder the terms:
-126 + -69b + 15b2 = 0

Solving
-126 + -69b + 15b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-42 + -23b + 5b2) = 0

Factor a trinomial.
3((-7 + -5b)(6 + -1b)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + -5b)' equal to zero and attempt to solve:

Simplifying
-7 + -5b = 0

Solving
-7 + -5b = 0

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

Add '7' to each side of the equation.
-7 + 7 + -5b = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5b = 0 + 7
-5b = 0 + 7

Combine like terms: 0 + 7 = 7
-5b = 7

Divide each side by '-5'.
b = -1.4

Simplifying
b = -1.4
Subproblem 2
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 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 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Solution
b = {-1.4, 6}