3x^2y-6xy-45y=0

Solution for 3x^2y-6xy-45y=0 equation:

Simplifying
3x2y + -6xy + -45y = 0

Reorder the terms:
-6xy + 3x2y + -45y = 0

Solving
-6xy + 3x2y + -45y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(-2x + x2 + -15) = 0

Factor a trinomial.
3y((x + -5)(x + 3)) = 0

Ignore the factor 3.
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 + -5)' equal to zero and attempt to solve:

Simplifying
x + -5 = 0

Reorder the terms:
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

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

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

Simplifying
x = 5
Subproblem 3
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
Solution
x = {5, -3}