6b^2=-5b+116

Solution for 6b^2=-5b+116 equation:

Simplifying
6b2 = -5b + 116

Reorder the terms:
6b2 = 116 + -5b

Solving
6b2 = 116 + -5b

Solving for variable 'b'.

Reorder the terms:
-116 + 5b + 6b2 = 116 + -5b + -116 + 5b

Reorder the terms:
-116 + 5b + 6b2 = 116 + -116 + -5b + 5b

Combine like terms: 116 + -116 = 0
-116 + 5b + 6b2 = 0 + -5b + 5b
-116 + 5b + 6b2 = -5b + 5b

Combine like terms: -5b + 5b = 0
-116 + 5b + 6b2 = 0

Factor a trinomial.
(-29 + -6b)(4 + -1b) = 0

Subproblem 1
Set the factor '(-29 + -6b)' equal to zero and attempt to solve:

Simplifying
-29 + -6b = 0

Solving
-29 + -6b = 0

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

Add '29' to each side of the equation.
-29 + 29 + -6b = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -6b = 0 + 29
-6b = 0 + 29

Combine like terms: 0 + 29 = 29
-6b = 29

Divide each side by '-6'.
b = -4.833333333

Simplifying
b = -4.833333333
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 = {-4.833333333, 4}