2b^2-b-378=0

Solution for 2b^2-b-378=0 equation:

Simplifying
2b2 + -1b + -378 = 0

Reorder the terms:
-378 + -1b + 2b2 = 0

Solving
-378 + -1b + 2b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-27 + -2b)(14 + -1b) = 0

Subproblem 1
Set the factor '(-27 + -2b)' equal to zero and attempt to solve:

Simplifying
-27 + -2b = 0

Solving
-27 + -2b = 0

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

Add '27' to each side of the equation.
-27 + 27 + -2b = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -2b = 0 + 27
-2b = 0 + 27

Combine like terms: 0 + 27 = 27
-2b = 27

Divide each side by '-2'.
b = -13.5

Simplifying
b = -13.5
Subproblem 2
Set the factor '(14 + -1b)' equal to zero and attempt to solve:

Simplifying
14 + -1b = 0

Solving
14 + -1b = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1b = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1b = 0 + -14
-1b = 0 + -14

Combine like terms: 0 + -14 = -14
-1b = -14

Divide each side by '-1'.
b = 14

Simplifying
b = 14
Solution
b = {-13.5, 14}