13-(2n+2)=(n+2)3n

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Solution for 13-(2n+2)=(n+2)3n equation: 


Simplifying
13 + -1(2n + 2) = (n + 2) * 3n

Reorder the terms:
13 + -1(2 + 2n) = (n + 2) * 3n
13 + (2 * -1 + 2n * -1) = (n + 2) * 3n
13 + (-2 + -2n) = (n + 2) * 3n

Combine like terms: 13 + -2 = 11
11 + -2n = (n + 2) * 3n

Reorder the terms:
11 + -2n = (2 + n) * 3n

Reorder the terms for easier multiplication:
11 + -2n = 3n(2 + n)
11 + -2n = (2 * 3n + n * 3n)
11 + -2n = (6n + 3n2)

Solving
11 + -2n = 6n + 3n2

Solving for variable 'n'.

Combine like terms: -2n + -6n = -8n
11 + -8n + -3n2 = 6n + 3n2 + -6n + -3n2

Reorder the terms:
11 + -8n + -3n2 = 6n + -6n + 3n2 + -3n2

Combine like terms: 6n + -6n = 0
11 + -8n + -3n2 = 0 + 3n2 + -3n2
11 + -8n + -3n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
11 + -8n + -3n2 = 0

Factor a trinomial.
(1 + -1n)(11 + 3n) = 0


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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 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 + -1n = 0 + -1

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

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

Divide each side by '-1'.
n = 1

Simplifying
n = 1

Subproblem 2
Set the factor '(11 + 3n)' equal to zero and attempt to solve:

Simplifying
11 + 3n = 0

Solving
11 + 3n = 0

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

Add '-11' to each side of the equation.
11 + -11 + 3n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 3n = 0 + -11
3n = 0 + -11

Combine like terms: 0 + -11 = -11
3n = -11

Divide each side by '3'.
n = -3.666666667

Simplifying
n = -3.666666667
Solution
n = {1, -3.666666667}

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