(8b^2-7b-6)-(5b^2+8b+12)=

Solution for (8b^2-7b-6)-(5b^2+8b+12)= equation:

Simplifying
(8b2 + -7b + -6) + -1(5b2 + 8b + 12) = 0

Reorder the terms:
(-6 + -7b + 8b2) + -1(5b2 + 8b + 12) = 0

Remove parenthesis around (-6 + -7b + 8b2)
-6 + -7b + 8b2 + -1(5b2 + 8b + 12) = 0

Reorder the terms:
-6 + -7b + 8b2 + -1(12 + 8b + 5b2) = 0
-6 + -7b + 8b2 + (12 * -1 + 8b * -1 + 5b2 * -1) = 0
-6 + -7b + 8b2 + (-12 + -8b + -5b2) = 0

Reorder the terms:
-6 + -12 + -7b + -8b + 8b2 + -5b2 = 0

Combine like terms: -6 + -12 = -18
-18 + -7b + -8b + 8b2 + -5b2 = 0

Combine like terms: -7b + -8b = -15b
-18 + -15b + 8b2 + -5b2 = 0

Combine like terms: 8b2 + -5b2 = 3b2
-18 + -15b + 3b2 = 0

Solving
-18 + -15b + 3b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -5b + b2) = 0

Factor a trinomial.
3((-1 + -1b)(6 + -1b)) = 0

Ignore the factor 3.
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 '(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
Solution
b = {-1, 6}