40xy^4-40xy^2z+10xz^2=0

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Solution for 40xy^4-40xy^2z+10xz^2=0 equation: 


Simplifying
40xy4 + -40xy2z + 10xz2 = 0

Reorder the terms:
-40xy2z + 40xy4 + 10xz2 = 0

Solving
-40xy2z + 40xy4 + 10xz2 = 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), '10x'.
10x(-4y2z + 4y4 + z2) = 0

Factor a trinomial.
10x((2y2 + -1z)(2y2 + -1z)) = 0

Ignore the factor 10.

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

Simplifying
2y2 + -1z = 0

Solving
2y2 + -1z = 0

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

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

Combine like terms: 2y2 + -2y2 = 0
0 + -1z = 0 + -2y2
-1z = 0 + -2y2
Remove the zero:
-1z = -2y2

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

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

Simplifying
0 = -2y2 + z

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

Simplifying
2y2 + -1z = 0

Solving
2y2 + -1z = 0

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

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

Combine like terms: 2y2 + -2y2 = 0
0 + -1z = 0 + -2y2
-1z = 0 + -2y2
Remove the zero:
-1z = -2y2

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

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

Simplifying
0 = -2y2 + z

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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