2xy^2+8xy-24x=0

Solution for 2xy^2+8xy-24x=0 equation:

Simplifying
2xy2 + 8xy + -24x = 0

Reorder the terms:
-24x + 8xy + 2xy2 = 0

Solving
-24x + 8xy + 2xy2 = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-12 + 4y + y2) = 0

Factor a trinomial.
2x((-6 + -1y)(2 + -1y)) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

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

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Add 'y' to each side of the equation.
-1y + y = 6 + y

Combine like terms: -1y + y = 0
0 = 6 + y

Simplifying
0 = 6 + y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 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 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Add 'y' to each side of the equation.
-1y + y = -2 + y

Combine like terms: -1y + y = 0
0 = -2 + y

Simplifying
0 = -2 + y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}