n+7n=n(n+x)

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Solution for n+7n=n(n+x) equation: 


Simplifying
n + 7n = n(n + x)

Combine like terms: n + 7n = 8n
8n = n(n + x)
8n = (n * n + x * n)

Reorder the terms:
8n = (nx + n2)
8n = (nx + n2)

Solving
8n = nx + n2

Solving for variable 'n'.

Reorder the terms:
8n + -1nx + -1n2 = nx + -1nx + n2 + -1n2

Combine like terms: nx + -1nx = 0
8n + -1nx + -1n2 = 0 + n2 + -1n2
8n + -1nx + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
8n + -1nx + -1n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(8 + -1x + -1n) = 0


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 '(8 + -1x + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1x + -1n = 0

Reorder the terms:
8 + -1n + -1x = 0

Solving
8 + -1n + -1x = 0

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

Add '-8' to each side of the equation.
8 + -1n + -8 + -1x = 0 + -8

Reorder the terms:
8 + -8 + -1n + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n + -1x = 0 + -8
-1n + -1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1n + -1x = -8

Add 'x' to each side of the equation.
-1n + -1x + x = -8 + x

Combine like terms: -1x + x = 0
-1n + 0 = -8 + x
-1n = -8 + x

Divide each side by '-1'.
n = 8 + -1x

Simplifying
n = 8 + -1x
Solution
n = {0, 8 + -1x}

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