4z^2(x+y)-21z(x+y)z^3=0

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Solution for 4z^2(x+y)-21z(x+y)z^3=0 equation: 


Simplifying
4z2(x + y) + -21z(x + y) * z3 = 0
(x * 4z2 + y * 4z2) + -21z(x + y) * z3 = 0
(4xz2 + 4yz2) + -21z(x + y) * z3 = 0

Reorder the terms for easier multiplication:
4xz2 + 4yz2 + -21z * z3(x + y) = 0

Multiply z * z3
4xz2 + 4yz2 + -21z4(x + y) = 0
4xz2 + 4yz2 + (x * -21z4 + y * -21z4) = 0
4xz2 + 4yz2 + (-21xz4 + -21yz4) = 0

Reorder the terms:
4xz2 + -21xz4 + 4yz2 + -21yz4 = 0

Solving
4xz2 + -21xz4 + 4yz2 + -21yz4 = 0

Solving for variable 'x'.

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

Add '-4yz2' to each side of the equation.
4xz2 + -21xz4 + 4yz2 + -4yz2 + -21yz4 = 0 + -4yz2

Combine like terms: 4yz2 + -4yz2 = 0
4xz2 + -21xz4 + 0 + -21yz4 = 0 + -4yz2
4xz2 + -21xz4 + -21yz4 = 0 + -4yz2
Remove the zero:
4xz2 + -21xz4 + -21yz4 = -4yz2

Add '21yz4' to each side of the equation.
4xz2 + -21xz4 + -21yz4 + 21yz4 = -4yz2 + 21yz4

Combine like terms: -21yz4 + 21yz4 = 0
4xz2 + -21xz4 + 0 = -4yz2 + 21yz4
4xz2 + -21xz4 = -4yz2 + 21yz4

Reorder the terms:
4xz2 + -21xz4 + 4yz2 + -21yz4 = -4yz2 + 4yz2 + 21yz4 + -21yz4

Combine like terms: -4yz2 + 4yz2 = 0
4xz2 + -21xz4 + 4yz2 + -21yz4 = 0 + 21yz4 + -21yz4
4xz2 + -21xz4 + 4yz2 + -21yz4 = 21yz4 + -21yz4

Combine like terms: 21yz4 + -21yz4 = 0
4xz2 + -21xz4 + 4yz2 + -21yz4 = 0

Factor out the Greatest Common Factor (GCF), 'z2'.
z2(4x + -21xz2 + 4y + -21yz2) = 0


Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Add '-1z2' to each side of the equation.
z2 + -1z2 = 0 + -1z2
Remove the zero:
0 = -1z2

Simplifying
0 = -1z2

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 '(4x + -21xz2 + 4y + -21yz2)' equal to zero and attempt to solve:

Simplifying
4x + -21xz2 + 4y + -21yz2 = 0

Solving
4x + -21xz2 + 4y + -21yz2 = 0

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

Add '-4y' to each side of the equation.
4x + -21xz2 + 4y + -4y + -21yz2 = 0 + -4y

Combine like terms: 4y + -4y = 0
4x + -21xz2 + 0 + -21yz2 = 0 + -4y
4x + -21xz2 + -21yz2 = 0 + -4y
Remove the zero:
4x + -21xz2 + -21yz2 = -4y

Add '21yz2' to each side of the equation.
4x + -21xz2 + -21yz2 + 21yz2 = -4y + 21yz2

Combine like terms: -21yz2 + 21yz2 = 0
4x + -21xz2 + 0 = -4y + 21yz2
4x + -21xz2 = -4y + 21yz2

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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