12x^3y^2+14x^2y-6x=

Solution for 12x^3y^2+14x^2y-6x= equation:

Simplifying
12x3y2 + 14x2y + -6x = 0

Reorder the terms:
-6x + 14x2y + 12x3y2 = 0

Solving
-6x + 14x2y + 12x3y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-3 + 7xy + 6x2y2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-3 + -2xy)' equal to zero and attempt to solve:

Simplifying
-3 + -2xy = 0

Solving
-3 + -2xy = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2xy = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2xy = 0 + 3
-2xy = 0 + 3

Combine like terms: 0 + 3 = 3
-2xy = 3

Divide each side by '-2y'.
x = -1.5y-1

Simplifying
x = -1.5y-1
Subproblem 3
Set the factor '(1 + -3xy)' equal to zero and attempt to solve:

Simplifying
1 + -3xy = 0

Solving
1 + -3xy = 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 + -3xy = 0 + -1

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

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

Divide each side by '-3y'.
x = 0.3333333333y-1

Simplifying
x = 0.3333333333y-1
Solution
x = {0, -1.5y-1, 0.3333333333y-1}