(n-8)(n+3)=n-8

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Solution for (n-8)(n+3)=n-8 equation: 


Simplifying
(n + -8)(n + 3) = n + -8

Reorder the terms:
(-8 + n)(n + 3) = n + -8

Reorder the terms:
(-8 + n)(3 + n) = n + -8

Multiply (-8 + n) * (3 + n)
(-8(3 + n) + n(3 + n)) = n + -8
((3 * -8 + n * -8) + n(3 + n)) = n + -8
((-24 + -8n) + n(3 + n)) = n + -8
(-24 + -8n + (3 * n + n * n)) = n + -8
(-24 + -8n + (3n + n2)) = n + -8

Combine like terms: -8n + 3n = -5n
(-24 + -5n + n2) = n + -8

Reorder the terms:
-24 + -5n + n2 = -8 + n

Solving
-24 + -5n + n2 = -8 + n

Solving for variable 'n'.

Reorder the terms:
-24 + 8 + -5n + -1n + n2 = -8 + n + 8 + -1n

Combine like terms: -24 + 8 = -16
-16 + -5n + -1n + n2 = -8 + n + 8 + -1n

Combine like terms: -5n + -1n = -6n
-16 + -6n + n2 = -8 + n + 8 + -1n

Reorder the terms:
-16 + -6n + n2 = -8 + 8 + n + -1n

Combine like terms: -8 + 8 = 0
-16 + -6n + n2 = 0 + n + -1n
-16 + -6n + n2 = n + -1n

Combine like terms: n + -1n = 0
-16 + -6n + n2 = 0

Factor a trinomial.
(-2 + -1n)(8 + -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 '(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 = {-2, 8}

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