b^2+4b-102=-6

Solution for b^2+4b-102=-6 equation:

Simplifying
b2 + 4b + -102 = -6

Reorder the terms:
-102 + 4b + b2 = -6

Solving
-102 + 4b + b2 = -6

Solving for variable 'b'.

Reorder the terms:
-102 + 6 + 4b + b2 = -6 + 6

Combine like terms: -102 + 6 = -96
-96 + 4b + b2 = -6 + 6

Combine like terms: -6 + 6 = 0
-96 + 4b + b2 = 0

Factor a trinomial.
(-12 + -1b)(8 + -1b) = 0

Subproblem 1
Set the factor '(-12 + -1b)' equal to zero and attempt to solve:

Simplifying
-12 + -1b = 0

Solving
-12 + -1b = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1b = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1b = 0 + 12
-1b = 0 + 12

Combine like terms: 0 + 12 = 12
-1b = 12

Divide each side by '-1'.
b = -12

Simplifying
b = -12
Subproblem 2
Set the factor '(8 + -1b)' equal to zero and attempt to solve:

Simplifying
8 + -1b = 0

Solving
8 + -1b = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1b = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1b = 0 + -8
-1b = 0 + -8

Combine like terms: 0 + -8 = -8
-1b = -8

Divide each side by '-1'.
b = 8

Simplifying
b = 8
Solution
b = {-12, 8}