n^2-9n-40=-8-5n

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Solution for n^2-9n-40=-8-5n equation: 


Simplifying
n2 + -9n + -40 = -8 + -5n

Reorder the terms:
-40 + -9n + n2 = -8 + -5n

Solving
-40 + -9n + n2 = -8 + -5n

Solving for variable 'n'.

Reorder the terms:
-40 + 8 + -9n + 5n + n2 = -8 + -5n + 8 + 5n

Combine like terms: -40 + 8 = -32
-32 + -9n + 5n + n2 = -8 + -5n + 8 + 5n

Combine like terms: -9n + 5n = -4n
-32 + -4n + n2 = -8 + -5n + 8 + 5n

Reorder the terms:
-32 + -4n + n2 = -8 + 8 + -5n + 5n

Combine like terms: -8 + 8 = 0
-32 + -4n + n2 = 0 + -5n + 5n
-32 + -4n + n2 = -5n + 5n

Combine like terms: -5n + 5n = 0
-32 + -4n + n2 = 0

Factor a trinomial.
(-4 + -1n)(8 + -1n) = 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 '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {-4, 8}

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