6n^2+16n=8n-12+5n^2

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Solution for 6n^2+16n=8n-12+5n^2 equation: 


Simplifying
6n2 + 16n = 8n + -12 + 5n2

Reorder the terms:
16n + 6n2 = 8n + -12 + 5n2

Reorder the terms:
16n + 6n2 = -12 + 8n + 5n2

Solving
16n + 6n2 = -12 + 8n + 5n2

Solving for variable 'n'.

Reorder the terms:
12 + 16n + -8n + 6n2 + -5n2 = -12 + 8n + 5n2 + 12 + -8n + -5n2

Combine like terms: 16n + -8n = 8n
12 + 8n + 6n2 + -5n2 = -12 + 8n + 5n2 + 12 + -8n + -5n2

Combine like terms: 6n2 + -5n2 = 1n2
12 + 8n + 1n2 = -12 + 8n + 5n2 + 12 + -8n + -5n2

Reorder the terms:
12 + 8n + 1n2 = -12 + 12 + 8n + -8n + 5n2 + -5n2

Combine like terms: -12 + 12 = 0
12 + 8n + 1n2 = 0 + 8n + -8n + 5n2 + -5n2
12 + 8n + 1n2 = 8n + -8n + 5n2 + -5n2

Combine like terms: 8n + -8n = 0
12 + 8n + 1n2 = 0 + 5n2 + -5n2
12 + 8n + 1n2 = 5n2 + -5n2

Combine like terms: 5n2 + -5n2 = 0
12 + 8n + 1n2 = 0

Factor a trinomial.
(6 + n)(2 + n) = 0


Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6

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

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

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

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

Simplifying
n = -2
Solution
n = {-6, -2}

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