12b^2-28b-24=0

Solution for 12b^2-28b-24=0 equation:

Simplifying
12b2 + -28b + -24 = 0

Reorder the terms:
-24 + -28b + 12b2 = 0

Solving
-24 + -28b + 12b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -7b + 3b2) = 0

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

Ignore the factor 4.
Subproblem 1
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
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 = {-0.6666666667, 3}