42b^2-10b-12=0

Solution for 42b^2-10b-12=0 equation:

Simplifying
42b2 + -10b + -12 = 0

Reorder the terms:
-12 + -10b + 42b2 = 0

Solving
-12 + -10b + 42b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -5b + 21b2) = 0

Factor a trinomial.
2((-3 + -7b)(2 + -3b)) = 0

Ignore the factor 2.
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 '(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 = {-0.4285714286, 0.6666666667}