7b^2-54b-22=-6

Solution for 7b^2-54b-22=-6 equation:

Simplifying
7b2 + -54b + -22 = -6

Reorder the terms:
-22 + -54b + 7b2 = -6

Solving
-22 + -54b + 7b2 = -6

Solving for variable 'b'.

Reorder the terms:
-22 + 6 + -54b + 7b2 = -6 + 6

Combine like terms: -22 + 6 = -16
-16 + -54b + 7b2 = -6 + 6

Combine like terms: -6 + 6 = 0
-16 + -54b + 7b2 = 0

Factor a trinomial.
(-2 + -7b)(8 + -1b) = 0

Subproblem 1
Set the factor '(-2 + -7b)' equal to zero and attempt to solve:

Simplifying
-2 + -7b = 0

Solving
-2 + -7b = 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 + -7b = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7b = 0 + 2
-7b = 0 + 2

Combine like terms: 0 + 2 = 2
-7b = 2

Divide each side by '-7'.
b = -0.2857142857

Simplifying
b = -0.2857142857
Subproblem 2
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
Solution
b = {-0.2857142857, 8}