b^2-3b-11=-7

Solution for b^2-3b-11=-7 equation:

Simplifying
b2 + -3b + -11 = -7

Reorder the terms:
-11 + -3b + b2 = -7

Solving
-11 + -3b + b2 = -7

Solving for variable 'b'.

Reorder the terms:
-11 + 7 + -3b + b2 = -7 + 7

Combine like terms: -11 + 7 = -4
-4 + -3b + b2 = -7 + 7

Combine like terms: -7 + 7 = 0
-4 + -3b + b2 = 0

Factor a trinomial.
(-1 + -1b)(4 + -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 '(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
Solution
b = {-1, 4}