10x^3y^2-28x^2y^2-6xy^2=0

Solution for 10x^3y^2-28x^2y^2-6xy^2=0 equation:

Simplifying
10x3y2 + -28x2y2 + -6xy2 = 0

Reorder the terms:
-6xy2 + -28x2y2 + 10x3y2 = 0

Solving
-6xy2 + -28x2y2 + 10x3y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2xy2'.
2xy2(-3 + -14x + 5x2) = 0

Factor a trinomial.
2xy2((-1 + -5x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'xy2' equal to zero and attempt to solve:

Simplifying
xy2 = 0

Solving
xy2 = 0

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

Simplifying
xy2 = 0

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 '(-1 + -5x)' equal to zero and attempt to solve:

Simplifying
-1 + -5x = 0

Solving
-1 + -5x = 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 + -5x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5x = 0 + 1
-5x = 0 + 1

Combine like terms: 0 + 1 = 1
-5x = 1

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2
Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

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

Simplifying
x = 3
Solution
x = {-0.2, 3}