14b^2-34b-24=0

Solution for 14b^2-34b-24=0 equation:

Simplifying
14b2 + -34b + -24 = 0

Reorder the terms:
-24 + -34b + 14b2 = 0

Solving
-24 + -34b + 14b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -17b + 7b2) = 0

Factor a trinomial.
2((-4 + -7b)(3 + -1b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -7b)' equal to zero and attempt to solve:

Simplifying
-4 + -7b = 0

Solving
-4 + -7b = 0

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

Add '4' to each side of the equation.
-4 + 4 + -7b = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -7b = 0 + 4
-7b = 0 + 4

Combine like terms: 0 + 4 = 4
-7b = 4

Divide each side by '-7'.
b = -0.5714285714

Simplifying
b = -0.5714285714
Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 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 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {-0.5714285714, 3}