42b^2-17b-15=0

Solution for 42b^2-17b-15=0 equation:

Simplifying
42b2 + -17b + -15 = 0

Reorder the terms:
-15 + -17b + 42b2 = 0

Solving
-15 + -17b + 42b2 = 0

Solving for variable 'b'.

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

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

Simplifying
-3 + -7b = 0

Solving
-3 + -7b = 0

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

Add '3' to each side of the equation.
-3 + 3 + -7b = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7b = 0 + 3
-7b = 0 + 3

Combine like terms: 0 + 3 = 3
-7b = 3

Divide each side by '-7'.
b = -0.4285714286

Simplifying
b = -0.4285714286
Subproblem 2
Set the factor '(5 + -6b)' equal to zero and attempt to solve:

Simplifying
5 + -6b = 0

Solving
5 + -6b = 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 + -6b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6b = 0 + -5
-6b = 0 + -5

Combine like terms: 0 + -5 = -5
-6b = -5

Divide each side by '-6'.
b = 0.8333333333

Simplifying
b = 0.8333333333
Solution
b = {-0.4285714286, 0.8333333333}