n^2+3n-54=(n+9)

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Solution for n^2+3n-54=(n+9) equation: 


Simplifying
n2 + 3n + -54 = (n + 9)

Reorder the terms:
-54 + 3n + n2 = (n + 9)

Reorder the terms:
-54 + 3n + n2 = (9 + n)

Remove parenthesis around (9 + n)
-54 + 3n + n2 = 9 + n

Solving
-54 + 3n + n2 = 9 + n

Solving for variable 'n'.

Reorder the terms:
-54 + -9 + 3n + -1n + n2 = 9 + n + -9 + -1n

Combine like terms: -54 + -9 = -63
-63 + 3n + -1n + n2 = 9 + n + -9 + -1n

Combine like terms: 3n + -1n = 2n
-63 + 2n + n2 = 9 + n + -9 + -1n

Reorder the terms:
-63 + 2n + n2 = 9 + -9 + n + -1n

Combine like terms: 9 + -9 = 0
-63 + 2n + n2 = 0 + n + -1n
-63 + 2n + n2 = n + -1n

Combine like terms: n + -1n = 0
-63 + 2n + n2 = 0

Factor a trinomial.
(-9 + -1n)(7 + -1n) = 0


Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve:

Simplifying
-9 + -1n = 0

Solving
-9 + -1n = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1n = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1n = 0 + 9
-1n = 0 + 9

Combine like terms: 0 + 9 = 9
-1n = 9

Divide each side by '-1'.
n = -9

Simplifying
n = -9

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 = {-9, 7}

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