(n+2)((n+2)-9)=0

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Solution for (n+2)((n+2)-9)=0 equation: 


Simplifying
(n + 2)((n + 2) + -9) = 0

Reorder the terms:
(2 + n)((n + 2) + -9) = 0

Reorder the terms:
(2 + n)((2 + n) + -9) = 0

Remove parenthesis around (2 + n)
(2 + n)(2 + n + -9) = 0

Reorder the terms:
(2 + n)(2 + -9 + n) = 0

Combine like terms: 2 + -9 = -7
(2 + n)(-7 + n) = 0

Multiply (2 + n) * (-7 + n)
(2(-7 + n) + n(-7 + n)) = 0
((-7 * 2 + n * 2) + n(-7 + n)) = 0
((-14 + 2n) + n(-7 + n)) = 0
(-14 + 2n + (-7 * n + n * n)) = 0
(-14 + 2n + (-7n + n2)) = 0

Combine like terms: 2n + -7n = -5n
(-14 + -5n + n2) = 0

Solving
-14 + -5n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-2 + -1n)(7 + -1n) = 0


Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 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 + -1n = 0 + 2

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

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

Divide each side by '-1'.
n = -2

Simplifying
n = -2

Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 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 + -1n = 0 + -7

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

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

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-2, 7}

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