7b^2-84=-7b

Solution for 7b^2-84=-7b equation:

Simplifying
7b2 + -84 = -7b

Reorder the terms:
-84 + 7b2 = -7b

Solving
-84 + 7b2 = -7b

Solving for variable 'b'.

Reorder the terms:
-84 + 7b + 7b2 = -7b + 7b

Combine like terms: -7b + 7b = 0
-84 + 7b + 7b2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-12 + b + b2) = 0

Factor a trinomial.
7((-4 + -1b)(3 + -1b)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-4 + -1b)' equal to zero and attempt to solve:

Simplifying
-4 + -1b = 0

Solving
-4 + -1b = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1b = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1b = 0 + 4
-1b = 0 + 4

Combine like terms: 0 + 4 = 4
-1b = 4

Divide each side by '-1'.
b = -4

Simplifying
b = -4
Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {-4, 3}