y(x^2)-y(x+6)=0

Solution for y(x^2)-y(x+6)=0 equation:

Simplifying
y(x2) + -1y(x + 6) = 0

Multiply y * x2
x2y + -1y(x + 6) = 0

Reorder the terms:
x2y + -1y(6 + x) = 0
x2y + (6 * -1y + x * -1y) = 0

Reorder the terms:
x2y + (-1xy + -6y) = 0
x2y + (-1xy + -6y) = 0

Reorder the terms:
-1xy + x2y + -6y = 0

Solving
-1xy + x2y + -6y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1x + x2 + -6) = 0

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

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 '(x + -3)' equal to zero and attempt to solve:

Simplifying
x + -3 = 0

Reorder the terms:
-3 + x = 0

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

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

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

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

Simplifying
x + 2 = 0

Reorder the terms:
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {3, -2}