8b^2+24b-32=0

Solution for 8b^2+24b-32=0 equation:

Simplifying
8b2 + 24b + -32 = 0

Reorder the terms:
-32 + 24b + 8b2 = 0

Solving
-32 + 24b + 8b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-4 + 3b + b2) = 0

Factor a trinomial.
8((-4 + -1b)(1 + -1b)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-4 + -1b)' equal to zero and attempt to solve:

Simplifying
-4 + -1b = 0

Solving
-4 + -1b = 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 + -1b = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1b = 0 + 4
-1b = 0 + 4

Combine like terms: 0 + 4 = 4
-1b = 4

Divide each side by '-1'.
b = -4

Simplifying
b = -4
Subproblem 2
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
Solution
b = {-4, 1}