b^2-6b-33=7

Solution for b^2-6b-33=7 equation:

Simplifying
b2 + -6b + -33 = 7

Reorder the terms:
-33 + -6b + b2 = 7

Solving
-33 + -6b + b2 = 7

Solving for variable 'b'.

Reorder the terms:
-33 + -7 + -6b + b2 = 7 + -7

Combine like terms: -33 + -7 = -40
-40 + -6b + b2 = 7 + -7

Combine like terms: 7 + -7 = 0
-40 + -6b + b2 = 0

Factor a trinomial.
(-4 + -1b)(10 + -1b) = 0

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 '(10 + -1b)' equal to zero and attempt to solve:

Simplifying
10 + -1b = 0

Solving
10 + -1b = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1b = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1b = 0 + -10
-1b = 0 + -10

Combine like terms: 0 + -10 = -10
-1b = -10

Divide each side by '-1'.
b = 10

Simplifying
b = 10
Solution
b = {-4, 10}