(-3x)(2x^2+y^2-2)=0

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Solution for (-3x)(2x^2+y^2-2)=0 equation: 


Simplifying
(-3x)(2x2 + y2 + -2) = 0

Remove parenthesis around (-3x)
-3x(2x2 + y2 + -2) = 0

Reorder the terms:
-3x(-2 + 2x2 + y2) = 0
(-2 * -3x + 2x2 * -3x + y2 * -3x) = 0

Reorder the terms:
(6x + -3xy2 + -6x3) = 0
(6x + -3xy2 + -6x3) = 0

Solving
6x + -3xy2 + -6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(2 + -1y2 + -2x2) = 0

Ignore the factor 3.

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 '(2 + -1y2 + -2x2)' equal to zero and attempt to solve:

Simplifying
2 + -1y2 + -2x2 = 0

Reorder the terms:
2 + -2x2 + -1y2 = 0

Solving
2 + -2x2 + -1y2 = 0

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

Add '-2' to each side of the equation.
2 + -2x2 + -2 + -1y2 = 0 + -2

Reorder the terms:
2 + -2 + -2x2 + -1y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -2x2 + -1y2 = 0 + -2
-2x2 + -1y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-2x2 + -1y2 = -2

Add 'y2' to each side of the equation.
-2x2 + -1y2 + y2 = -2 + y2

Combine like terms: -1y2 + y2 = 0
-2x2 + 0 = -2 + y2
-2x2 = -2 + y2

Divide each side by '-2'.
x2 = 1 + -0.5y2

Simplifying
x2 = 1 + -0.5y2

The solution to this equation could not be determined.

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

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