5zn=7n+8nz

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Solution for 5zn=7n+8nz equation: 


Simplifying
5zn = 7n + 8nz

Solving
5nz = 7n + 8nz

Solving for variable 'n'.

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

Add '-7n' to each side of the equation.
-7n + 5nz = 7n + -7n + 8nz

Combine like terms: 7n + -7n = 0
-7n + 5nz = 0 + 8nz
-7n + 5nz = 8nz

Add '-8nz' to each side of the equation.
-7n + 5nz + -8nz = 8nz + -8nz

Combine like terms: 5nz + -8nz = -3nz
-7n + -3nz = 8nz + -8nz

Combine like terms: 8nz + -8nz = 0
-7n + -3nz = 0

Factor out the Greatest Common Factor (GCF), '-1n'.
-1n(7 + 3z) = 0

Ignore the factor -1.

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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(7 + 3z)' equal to zero and attempt to solve:

Simplifying
7 + 3z = 0

Solving
7 + 3z = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3z = 0 + -7
3z = 0 + -7

Combine like terms: 0 + -7 = -7
3z = -7

Add '-3z' to each side of the equation.
3z + -3z = -7 + -3z

Combine like terms: 3z + -3z = 0
0 = -7 + -3z

Simplifying
0 = -7 + -3z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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