3b^2+b-52=0

Solution for 3b^2+b-52=0 equation:

Simplifying
3b2 + b + -52 = 0

Reorder the terms:
-52 + b + 3b2 = 0

Solving
-52 + b + 3b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-13 + -3b)(4 + -1b) = 0

Subproblem 1
Set the factor '(-13 + -3b)' equal to zero and attempt to solve:

Simplifying
-13 + -3b = 0

Solving
-13 + -3b = 0

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

Add '13' to each side of the equation.
-13 + 13 + -3b = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -3b = 0 + 13
-3b = 0 + 13

Combine like terms: 0 + 13 = 13
-3b = 13

Divide each side by '-3'.
b = -4.333333333

Simplifying
b = -4.333333333
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 = {-4.333333333, 4}