8x^3y-42x^2y^2+10xy^3=0

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Solution for 8x^3y-42x^2y^2+10xy^3=0 equation: 


Simplifying
8x3y + -42x2y2 + 10xy3 = 0

Reorder the terms:
10xy3 + -42x2y2 + 8x3y = 0

Solving
10xy3 + -42x2y2 + 8x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2xy'.
2xy(5y2 + -21xy + 4x2) = 0

Factor a trinomial.
2xy((y + -4x)(5y + -1x)) = 0

Ignore the factor 2.

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

Simplifying
xy = 0

Solving
xy = 0

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

Simplifying
xy = 0

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 '(y + -4x)' equal to zero and attempt to solve:

Simplifying
y + -4x = 0

Reorder the terms:
-4x + y = 0

Solving
-4x + y = 0

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

Add '-1y' to each side of the equation.
-4x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
-4x + 0 = 0 + -1y
-4x = 0 + -1y
Remove the zero:
-4x = -1y

Divide each side by '-4'.
x = 0.25y

Simplifying
x = 0.25y

Subproblem 3
Set the factor '(5y + -1x)' equal to zero and attempt to solve:

Simplifying
5y + -1x = 0

Reorder the terms:
-1x + 5y = 0

Solving
-1x + 5y = 0

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

Add '-5y' to each side of the equation.
-1x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
-1x + 0 = 0 + -5y
-1x = 0 + -5y
Remove the zero:
-1x = -5y

Divide each side by '-1'.
x = 5y

Simplifying
x = 5y
Solution
x = {0.25y, 5y}

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