b^2+7b-1=7

Solution for b^2+7b-1=7 equation:

Simplifying
b2 + 7b + -1 = 7

Reorder the terms:
-1 + 7b + b2 = 7

Solving
-1 + 7b + b2 = 7

Solving for variable 'b'.

Reorder the terms:
-1 + -7 + 7b + b2 = 7 + -7

Combine like terms: -1 + -7 = -8
-8 + 7b + b2 = 7 + -7

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

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

Subproblem 1
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
Subproblem 2
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
Solution
b = {-8, 1}