8b^2=96-32b

Solution for 8b^2=96-32b equation:

Simplifying
8b2 = 96 + -32b

Solving
8b2 = 96 + -32b

Solving for variable 'b'.

Reorder the terms:
-96 + 32b + 8b2 = 96 + -32b + -96 + 32b

Reorder the terms:
-96 + 32b + 8b2 = 96 + -96 + -32b + 32b

Combine like terms: 96 + -96 = 0
-96 + 32b + 8b2 = 0 + -32b + 32b
-96 + 32b + 8b2 = -32b + 32b

Combine like terms: -32b + 32b = 0
-96 + 32b + 8b2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-12 + 4b + b2) = 0

Factor a trinomial.
8((-6 + -1b)(2 + -1b)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-6 + -1b)' equal to zero and attempt to solve:

Simplifying
-6 + -1b = 0

Solving
-6 + -1b = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1b = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1b = 0 + 6
-1b = 0 + 6

Combine like terms: 0 + 6 = 6
-1b = 6

Divide each side by '-1'.
b = -6

Simplifying
b = -6
Subproblem 2
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
Solution
b = {-6, 2}