6x^2-x-222=0

Solution for 6x^2-x-222=0 equation:

Simplifying
6x2 + -1x + -222 = 0

Reorder the terms:
-222 + -1x + 6x2 = 0

Solving
-222 + -1x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(37 + -6x) = 0

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 '(37 + -6x)' equal to zero and attempt to solve:

Simplifying
37 + -6x = 0

Solving
37 + -6x = 0

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

Add '-37' to each side of the equation.
37 + -37 + -6x = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -6x = 0 + -37
-6x = 0 + -37

Combine like terms: 0 + -37 = -37
-6x = -37

Divide each side by '-6'.
x = 6.166666667

Simplifying
x = 6.166666667
Solution
x = {-6, 6.166666667}