14x^2y^2+86xy^2-84y^2=0

Solution for 14x^2y^2+86xy^2-84y^2=0 equation:

Simplifying
14x2y2 + 86xy2 + -84y2 = 0

Reorder the terms:
86xy2 + 14x2y2 + -84y2 = 0

Solving
86xy2 + 14x2y2 + -84y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2y2'.
2y2(43x + 7x2 + -42) = 0

Factor a trinomial.
2y2((7x + -6)(x + 7)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Add '-1y2' to each side of the equation.
y2 + -1y2 = 0 + -1y2
Remove the zero:
0 = -1y2

Simplifying
0 = -1y2

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

Simplifying
7x + -6 = 0

Reorder the terms:
-6 + 7x = 0

Solving
-6 + 7x = 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 + 7x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 7x = 0 + 6
7x = 0 + 6

Combine like terms: 0 + 6 = 6
7x = 6

Divide each side by '7'.
x = 0.8571428571

Simplifying
x = 0.8571428571
Subproblem 3
Set the factor '(x + 7)' equal to zero and attempt to solve:

Simplifying
x + 7 = 0

Reorder the terms:
7 + x = 0

Solving
7 + x = 0

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

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

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

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

Simplifying
x = -7
Solution
x = {0.8571428571, -7}