6x^2-2x-228=0

Solution for 6x^2-2x-228=0 equation:

Simplifying
6x2 + -2x + -228 = 0

Reorder the terms:
-228 + -2x + 6x2 = 0

Solving
-228 + -2x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-114 + -1x + 3x2) = 0

Factor a trinomial.
2((-6 + -1x)(19 + -3x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

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

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

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

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

Simplifying
x = -6
Subproblem 2
Set the factor '(19 + -3x)' equal to zero and attempt to solve:

Simplifying
19 + -3x = 0

Solving
19 + -3x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -3x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -3x = 0 + -19
-3x = 0 + -19

Combine like terms: 0 + -19 = -19
-3x = -19

Divide each side by '-3'.
x = 6.333333333

Simplifying
x = 6.333333333
Solution
x = {-6, 6.333333333}