14b^2+7b-42=0

Solution for 14b^2+7b-42=0 equation:

Simplifying
14b2 + 7b + -42 = 0

Reorder the terms:
-42 + 7b + 14b2 = 0

Solving
-42 + 7b + 14b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + b + 2b2) = 0

Factor a trinomial.
7((-2 + -1b)(3 + -2b)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-2 + -1b)' equal to zero and attempt to solve:

Simplifying
-2 + -1b = 0

Solving
-2 + -1b = 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 + -1b = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1b = 0 + 2
-1b = 0 + 2

Combine like terms: 0 + 2 = 2
-1b = 2

Divide each side by '-1'.
b = -2

Simplifying
b = -2
Subproblem 2
Set the factor '(3 + -2b)' equal to zero and attempt to solve:

Simplifying
3 + -2b = 0

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

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

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

Divide each side by '-2'.
b = 1.5

Simplifying
b = 1.5
Solution
b = {-2, 1.5}