(15-n)*2=n^2+(n+2)

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Solution for (15-n)*2=n^2+(n+2) equation: 


Simplifying
(15 + -1n) * 2 = n2 + (n + 2)

Reorder the terms for easier multiplication:
2(15 + -1n) = n2 + (n + 2)
(15 * 2 + -1n * 2) = n2 + (n + 2)
(30 + -2n) = n2 + (n + 2)

Reorder the terms:
30 + -2n = n2 + (2 + n)

Remove parenthesis around (2 + n)
30 + -2n = n2 + 2 + n

Reorder the terms:
30 + -2n = 2 + n + n2

Solving
30 + -2n = 2 + n + n2

Solving for variable 'n'.

Reorder the terms:
30 + -2 + -2n + -1n + -1n2 = 2 + n + n2 + -2 + -1n + -1n2

Combine like terms: 30 + -2 = 28
28 + -2n + -1n + -1n2 = 2 + n + n2 + -2 + -1n + -1n2

Combine like terms: -2n + -1n = -3n
28 + -3n + -1n2 = 2 + n + n2 + -2 + -1n + -1n2

Reorder the terms:
28 + -3n + -1n2 = 2 + -2 + n + -1n + n2 + -1n2

Combine like terms: 2 + -2 = 0
28 + -3n + -1n2 = 0 + n + -1n + n2 + -1n2
28 + -3n + -1n2 = n + -1n + n2 + -1n2

Combine like terms: n + -1n = 0
28 + -3n + -1n2 = 0 + n2 + -1n2
28 + -3n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
28 + -3n + -1n2 = 0

Factor a trinomial.
(4 + -1n)(7 + n) = 0


Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4

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

Simplifying
7 + n = 0

Solving
7 + n = 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 + n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + n = 0 + -7
n = 0 + -7

Combine like terms: 0 + -7 = -7
n = -7

Simplifying
n = -7
Solution
n = {4, -7}

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