b^2-4b-7=5

Solution for b^2-4b-7=5 equation:

Simplifying
b2 + -4b + -7 = 5

Reorder the terms:
-7 + -4b + b2 = 5

Solving
-7 + -4b + b2 = 5

Solving for variable 'b'.

Reorder the terms:
-7 + -5 + -4b + b2 = 5 + -5

Combine like terms: -7 + -5 = -12
-12 + -4b + b2 = 5 + -5

Combine like terms: 5 + -5 = 0
-12 + -4b + b2 = 0

Factor a trinomial.
(-2 + -1b)(6 + -1b) = 0

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

Simplifying
-2 + -1b = 0

Solving
-2 + -1b = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1b = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1b = 0 + 2
-1b = 0 + 2

Combine like terms: 0 + 2 = 2
-1b = 2

Divide each side by '-1'.
b = -2

Simplifying
b = -2
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 = {-2, 6}