3b^2+b=102

Solution for 3b^2+b=102 equation:

Simplifying
3b2 + b = 102

Reorder the terms:
b + 3b2 = 102

Solving
b + 3b2 = 102

Solving for variable 'b'.

Reorder the terms:
-102 + b + 3b2 = 102 + -102

Combine like terms: 102 + -102 = 0
-102 + b + 3b2 = 0

Factor a trinomial.
(-6 + -1b)(17 + -3b) = 0

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

Simplifying
-6 + -1b = 0

Solving
-6 + -1b = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1b = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1b = 0 + 6
-1b = 0 + 6

Combine like terms: 0 + 6 = 6
-1b = 6

Divide each side by '-1'.
b = -6

Simplifying
b = -6
Subproblem 2
Set the factor '(17 + -3b)' equal to zero and attempt to solve:

Simplifying
17 + -3b = 0

Solving
17 + -3b = 0

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

Add '-17' to each side of the equation.
17 + -17 + -3b = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -3b = 0 + -17
-3b = 0 + -17

Combine like terms: 0 + -17 = -17
-3b = -17

Divide each side by '-3'.
b = 5.666666667

Simplifying
b = 5.666666667
Solution
b = {-6, 5.666666667}