14x^2y+6xy-8y=0

Solution for 14x^2y+6xy-8y=0 equation:

Simplifying
14x2y + 6xy + -8y = 0

Reorder the terms:
6xy + 14x2y + -8y = 0

Solving
6xy + 14x2y + -8y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(3x + 7x2 + -4) = 0

Factor a trinomial.
2y((7x + -4)(x + 1)) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(7x + -4)' equal to zero and attempt to solve:

Simplifying
7x + -4 = 0

Reorder the terms:
-4 + 7x = 0

Solving
-4 + 7x = 0

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

Add '4' to each side of the equation.
-4 + 4 + 7x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 7x = 0 + 4
7x = 0 + 4

Combine like terms: 0 + 4 = 4
7x = 4

Divide each side by '7'.
x = 0.5714285714

Simplifying
x = 0.5714285714
Subproblem 3
Set the factor '(x + 1)' equal to zero and attempt to solve:

Simplifying
x + 1 = 0

Reorder the terms:
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {0.5714285714, -1}