6a^2+a-57=0

Solution for 6a^2+a-57=0 equation:

Simplifying
6a2 + a + -57 = 0

Reorder the terms:
-57 + a + 6a2 = 0

Solving
-57 + a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-19 + -6a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-19 + -6a)' equal to zero and attempt to solve:

Simplifying
-19 + -6a = 0

Solving
-19 + -6a = 0

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

Add '19' to each side of the equation.
-19 + 19 + -6a = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -6a = 0 + 19
-6a = 0 + 19

Combine like terms: 0 + 19 = 19
-6a = 19

Divide each side by '-6'.
a = -3.166666667

Simplifying
a = -3.166666667
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

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

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

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-3.166666667, 3}