-n^2+8n+4=7n+4-2n^2

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Solution for -n^2+8n+4=7n+4-2n^2 equation: 


Simplifying
-1n2 + 8n + 4 = 7n + 4 + -2n2

Reorder the terms:
4 + 8n + -1n2 = 7n + 4 + -2n2

Reorder the terms:
4 + 8n + -1n2 = 4 + 7n + -2n2

Add '-4' to each side of the equation.
4 + 8n + -4 + -1n2 = 4 + 7n + -4 + -2n2

Reorder the terms:
4 + -4 + 8n + -1n2 = 4 + 7n + -4 + -2n2

Combine like terms: 4 + -4 = 0
0 + 8n + -1n2 = 4 + 7n + -4 + -2n2
8n + -1n2 = 4 + 7n + -4 + -2n2

Reorder the terms:
8n + -1n2 = 4 + -4 + 7n + -2n2

Combine like terms: 4 + -4 = 0
8n + -1n2 = 0 + 7n + -2n2
8n + -1n2 = 7n + -2n2

Solving
8n + -1n2 = 7n + -2n2

Solving for variable 'n'.

Reorder the terms:
8n + -7n + -1n2 + 2n2 = 7n + -2n2 + -7n + 2n2

Combine like terms: 8n + -7n = 1n
1n + -1n2 + 2n2 = 7n + -2n2 + -7n + 2n2

Combine like terms: -1n2 + 2n2 = 1n2
1n + 1n2 = 7n + -2n2 + -7n + 2n2

Reorder the terms:
1n + 1n2 = 7n + -7n + -2n2 + 2n2

Combine like terms: 7n + -7n = 0
1n + 1n2 = 0 + -2n2 + 2n2
1n + 1n2 = -2n2 + 2n2

Combine like terms: -2n2 + 2n2 = 0
1n + 1n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(1 + n) = 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 '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

Simplifying
n = -1
Solution
n = {0, -1}

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