7b^2-7b-34=8

Solution for 7b^2-7b-34=8 equation:

Simplifying
7b2 + -7b + -34 = 8

Reorder the terms:
-34 + -7b + 7b2 = 8

Solving
-34 + -7b + 7b2 = 8

Solving for variable 'b'.

Reorder the terms:
-34 + -8 + -7b + 7b2 = 8 + -8

Combine like terms: -34 + -8 = -42
-42 + -7b + 7b2 = 8 + -8

Combine like terms: 8 + -8 = 0
-42 + -7b + 7b2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + -1b + b2) = 0

Factor a trinomial.
7((-2 + -1b)(3 + -1b)) = 0

Ignore the factor 7.
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 '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {-2, 3}