12x^2-22x-4=0

Solution for 12x^2-22x-4=0 equation:

Simplifying
12x2 + -22x + -4 = 0

Reorder the terms:
-4 + -22x + 12x2 = 0

Solving
-4 + -22x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -11x + 6x2) = 0

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

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

Simplifying
-1 + -6x = 0

Solving
-1 + -6x = 0

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

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

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

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

Divide each side by '-6'.
x = -0.1666666667

Simplifying
x = -0.1666666667
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.1666666667, 2}