3x^2y+y^3=42

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Solution for 3x^2y+y^3=42 equation: 


Simplifying
3x2y + y3 = 42

Solving
3x2y + y3 = 42

Solving for variable 'x'.

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

Add '-1y3' to each side of the equation.
3x2y + y3 + -1y3 = 42 + -1y3

Combine like terms: y3 + -1y3 = 0
3x2y + 0 = 42 + -1y3
3x2y = 42 + -1y3

Divide each side by '3y'.
x2 = 14y-1 + -0.3333333333y2

Simplifying
x2 = 14y-1 + -0.3333333333y2

Reorder the terms:
x2 + -14y-1 + 0.3333333333y2 = 14y-1 + -14y-1 + -0.3333333333y2 + 0.3333333333y2

Combine like terms: 14y-1 + -14y-1 = 0
x2 + -14y-1 + 0.3333333333y2 = 0 + -0.3333333333y2 + 0.3333333333y2
x2 + -14y-1 + 0.3333333333y2 = -0.3333333333y2 + 0.3333333333y2

Combine like terms: -0.3333333333y2 + 0.3333333333y2 = 0.0000000000
x2 + -14y-1 + 0.3333333333y2 = 0.0000000000

Factor out the Greatest Common Factor (GCF), 'y-1'.
y-1(x2y + -14 + 0.3333333333y3) = 0.0000000000


Subproblem 1
Set the factor 'y-1' equal to zero and attempt to solve:

Simplifying
y-1 = 0

Solving
y-1 = 0

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

Add '-1y-1' to each side of the equation.
y-1 + -1y-1 = 0 + -1y-1
Remove the zero:
0 = -1y-1

Simplifying
0 = -1y-1

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 '(x2y + -14 + 0.3333333333y3)' equal to zero and attempt to solve:

Simplifying
x2y + -14 + 0.3333333333y3 = 0

Reorder the terms:
-14 + x2y + 0.3333333333y3 = 0

Solving
-14 + x2y + 0.3333333333y3 = 0

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

Add '14' to each side of the equation.
-14 + x2y + 14 + 0.3333333333y3 = 0 + 14

Reorder the terms:
-14 + 14 + x2y + 0.3333333333y3 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + x2y + 0.3333333333y3 = 0 + 14
x2y + 0.3333333333y3 = 0 + 14

Combine like terms: 0 + 14 = 14
x2y + 0.3333333333y3 = 14

Add '-0.3333333333y3' to each side of the equation.
x2y + 0.3333333333y3 + -0.3333333333y3 = 14 + -0.3333333333y3

Combine like terms: 0.3333333333y3 + -0.3333333333y3 = 0.0000000000
x2y + 0.0000000000 = 14 + -0.3333333333y3
x2y = 14 + -0.3333333333y3

Divide each side by 'y'.
x2 = 14y-1 + -0.3333333333y2

Simplifying
x2 = 14y-1 + -0.3333333333y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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