4b^2-24b-28=0

Solution for 4b^2-24b-28=0 equation:

Simplifying
4b2 + -24b + -28 = 0

Reorder the terms:
-28 + -24b + 4b2 = 0

Solving
-28 + -24b + 4b2 = 0

Solving for variable 'b'.

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

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

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

Simplifying
-1 + -1b = 0

Solving
-1 + -1b = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1b = 0 + 1

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

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

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

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

Simplifying
7 + -1b = 0

Solving
7 + -1b = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1b = 0 + -7
-1b = 0 + -7

Combine like terms: 0 + -7 = -7
-1b = -7

Divide each side by '-1'.
b = 7

Simplifying
b = 7
Solution
b = {-1, 7}