45xy^4-30xy^2z+5xz^2=0

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Solution for 45xy^4-30xy^2z+5xz^2=0 equation: 


Simplifying
45xy4 + -30xy2z + 5xz2 = 0

Reorder the terms:
-30xy2z + 45xy4 + 5xz2 = 0

Solving
-30xy2z + 45xy4 + 5xz2 = 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), '5x'.
5x(-6y2z + 9y4 + z2) = 0

Factor a trinomial.
5x((3y2 + -1z)(3y2 + -1z)) = 0

Ignore the factor 5.

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 '(3y2 + -1z)' equal to zero and attempt to solve:

Simplifying
3y2 + -1z = 0

Solving
3y2 + -1z = 0

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

Add '-3y2' to each side of the equation.
3y2 + -3y2 + -1z = 0 + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 + -1z = 0 + -3y2
-1z = 0 + -3y2
Remove the zero:
-1z = -3y2

Add 'z' to each side of the equation.
-1z + z = -3y2 + z

Combine like terms: -1z + z = 0
0 = -3y2 + z

Simplifying
0 = -3y2 + 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 '(3y2 + -1z)' equal to zero and attempt to solve:

Simplifying
3y2 + -1z = 0

Solving
3y2 + -1z = 0

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

Add '-3y2' to each side of the equation.
3y2 + -3y2 + -1z = 0 + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 + -1z = 0 + -3y2
-1z = 0 + -3y2
Remove the zero:
-1z = -3y2

Add 'z' to each side of the equation.
-1z + z = -3y2 + z

Combine like terms: -1z + z = 0
0 = -3y2 + z

Simplifying
0 = -3y2 + 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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