16x^3y^4+14x^2y^2z+3xz^2=0

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Solution for 16x^3y^4+14x^2y^2z+3xz^2=0 equation: 


Simplifying
16x3y4 + 14x2y2z + 3xz2 = 0

Reorder the terms:
3xz2 + 14x2y2z + 16x3y4 = 0

Solving
3xz2 + 14x2y2z + 16x3y4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(3z2 + 14xy2z + 16x2y4) = 0

Factor a trinomial.
x((z + 2xy2)(3z + 8xy2)) = 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 '(z + 2xy2)' equal to zero and attempt to solve:

Simplifying
z + 2xy2 = 0

Reorder the terms:
2xy2 + z = 0

Solving
2xy2 + z = 0

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

Add '-1z' to each side of the equation.
2xy2 + z + -1z = 0 + -1z

Combine like terms: z + -1z = 0
2xy2 + 0 = 0 + -1z
2xy2 = 0 + -1z
Remove the zero:
2xy2 = -1z

Divide each side by '2y2'.
x = -0.5y-2z

Simplifying
x = -0.5y-2z

Subproblem 3
Set the factor '(3z + 8xy2)' equal to zero and attempt to solve:

Simplifying
3z + 8xy2 = 0

Reorder the terms:
8xy2 + 3z = 0

Solving
8xy2 + 3z = 0

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

Add '-3z' to each side of the equation.
8xy2 + 3z + -3z = 0 + -3z

Combine like terms: 3z + -3z = 0
8xy2 + 0 = 0 + -3z
8xy2 = 0 + -3z
Remove the zero:
8xy2 = -3z

Divide each side by '8y2'.
x = -0.375y-2z

Simplifying
x = -0.375y-2z
Solution
x = {0, -0.5y-2z, -0.375y-2z}

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