b^2=84-8b

Solution for b^2=84-8b equation:

Simplifying
b2 = 84 + -8b

Solving
b2 = 84 + -8b

Solving for variable 'b'.

Reorder the terms:
-84 + 8b + b2 = 84 + -8b + -84 + 8b

Reorder the terms:
-84 + 8b + b2 = 84 + -84 + -8b + 8b

Combine like terms: 84 + -84 = 0
-84 + 8b + b2 = 0 + -8b + 8b
-84 + 8b + b2 = -8b + 8b

Combine like terms: -8b + 8b = 0
-84 + 8b + b2 = 0

Factor a trinomial.
(-14 + -1b)(6 + -1b) = 0

Subproblem 1
Set the factor '(-14 + -1b)' equal to zero and attempt to solve:

Simplifying
-14 + -1b = 0

Solving
-14 + -1b = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1b = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1b = 0 + 14
-1b = 0 + 14

Combine like terms: 0 + 14 = 14
-1b = 14

Divide each side by '-1'.
b = -14

Simplifying
b = -14
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 = {-14, 6}