0=yx^3-3x

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Solution for 0=yx^3-3x equation:


Simplifying
0 = yx3 + -3x

Reorder the terms:
0 = -3x + x3y

Solving
0 = -3x + x3y

Solving for variable 'x'.
Remove the zero:
3x + -1x3y = -3x + x3y + 3x + -1x3y

Reorder the terms:
3x + -1x3y = -3x + 3x + x3y + -1x3y

Combine like terms: -3x + 3x = 0
3x + -1x3y = 0 + x3y + -1x3y
3x + -1x3y = x3y + -1x3y

Combine like terms: x3y + -1x3y = 0
3x + -1x3y = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + -1x2y) = 0

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 '(3 + -1x2y)' equal to zero and attempt to solve: Simplifying 3 + -1x2y = 0 Solving 3 + -1x2y = 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 + -1x2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x2y = 0 + -3 -1x2y = 0 + -3 Combine like terms: 0 + -3 = -3 -1x2y = -3 Divide each side by '-1y'. x2 = 3y-1 Simplifying x2 = 3y-1 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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