n^2-8n-9=2n(n-9)

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Solution for n^2-8n-9=2n(n-9) equation: 


Simplifying
n2 + -8n + -9 = 2n(n + -9)

Reorder the terms:
-9 + -8n + n2 = 2n(n + -9)

Reorder the terms:
-9 + -8n + n2 = 2n(-9 + n)
-9 + -8n + n2 = (-9 * 2n + n * 2n)
-9 + -8n + n2 = (-18n + 2n2)

Solving
-9 + -8n + n2 = -18n + 2n2

Solving for variable 'n'.

Reorder the terms:
-9 + -8n + 18n + n2 + -2n2 = -18n + 2n2 + 18n + -2n2

Combine like terms: -8n + 18n = 10n
-9 + 10n + n2 + -2n2 = -18n + 2n2 + 18n + -2n2

Combine like terms: n2 + -2n2 = -1n2
-9 + 10n + -1n2 = -18n + 2n2 + 18n + -2n2

Reorder the terms:
-9 + 10n + -1n2 = -18n + 18n + 2n2 + -2n2

Combine like terms: -18n + 18n = 0
-9 + 10n + -1n2 = 0 + 2n2 + -2n2
-9 + 10n + -1n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-9 + 10n + -1n2 = 0

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


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

Simplifying
-9 + n = 0

Solving
-9 + n = 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 + n = 0 + 9

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

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

Simplifying
n = 9

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
Solution
n = {9, 1}

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