6b^2-46b-16=0

Solution for 6b^2-46b-16=0 equation:

Simplifying
6b2 + -46b + -16 = 0

Reorder the terms:
-16 + -46b + 6b2 = 0

Solving
-16 + -46b + 6b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -23b + 3b2) = 0

Factor a trinomial.
2((-1 + -3b)(8 + -1b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -3b)' equal to zero and attempt to solve:

Simplifying
-1 + -3b = 0

Solving
-1 + -3b = 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 + -3b = 0 + 1

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

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

Divide each side by '-3'.
b = -0.3333333333

Simplifying
b = -0.3333333333
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 = {-0.3333333333, 8}