b^2=7b+8

Solution for b^2=7b+8 equation:

Simplifying
b2 = 7b + 8

Reorder the terms:
b2 = 8 + 7b

Solving
b2 = 8 + 7b

Solving for variable 'b'.

Reorder the terms:
-8 + -7b + b2 = 8 + 7b + -8 + -7b

Reorder the terms:
-8 + -7b + b2 = 8 + -8 + 7b + -7b

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

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

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

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 '(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 = {-1, 8}