-3b^2+3b+96=0

Solution for -3b^2+3b+96=0 equation:

Simplifying
-3b2 + 3b + 96 = 0

Reorder the terms:
96 + 3b + -3b2 = 0

Solving
96 + 3b + -3b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(32 + b + -1b2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(32 + b + -1b2)' equal to zero and attempt to solve:

Simplifying
32 + b + -1b2 = 0

Solving
32 + b + -1b2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-32 + -1b + b2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -1b + 32 + b2 = 0 + 32

Reorder the terms:
-32 + 32 + -1b + b2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -1b + b2 = 0 + 32
-1b + b2 = 0 + 32

Combine like terms: 0 + 32 = 32
-1b + b2 = 32

The b term is b.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1b + 0.25 + b2 = 32 + 0.25

Reorder the terms:
0.25 + -1b + b2 = 32 + 0.25

Combine like terms: 32 + 0.25 = 32.25
0.25 + -1b + b2 = 32.25

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(b + 0.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
b + 0.5 = 5.678908346

Simplifying
b + 0.5 = 5.678908346

Reorder the terms:
0.5 + b = 5.678908346

Solving
0.5 + b = 5.678908346

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = 5.678908346 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = 5.678908346 + -0.5
b = 5.678908346 + -0.5

Combine like terms: 5.678908346 + -0.5 = 5.178908346
b = 5.178908346

Simplifying
b = 5.178908346

Subproblem 2
b + 0.5 = -5.678908346

Simplifying
b + 0.5 = -5.678908346

Reorder the terms:
0.5 + b = -5.678908346

Solving
0.5 + b = -5.678908346

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = -5.678908346 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = -5.678908346 + -0.5
b = -5.678908346 + -0.5

Combine like terms: -5.678908346 + -0.5 = -6.178908346
b = -6.178908346

Simplifying
b = -6.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {5.178908346, -6.178908346}
Solution
b = {5.178908346, -6.178908346}