o(n)=n*n+n

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Solution for o(n)=n*n+n equation:


Simplifying
o(n) = n * n + n

Multiply o * n
no = n * n + n

Multiply n * n
no = n2 + n

Reorder the terms:
no = n + n2

Solving
no = n + n2

Solving for variable 'n'.

Reorder the terms:
-1n + no + -1n2 = n + n2 + -1n + -1n2

Reorder the terms:
-1n + no + -1n2 = n + -1n + n2 + -1n2

Combine like terms: n + -1n = 0
-1n + no + -1n2 = 0 + n2 + -1n2
-1n + no + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-1n + no + -1n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1 + o + -1n) = 0

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0

Subproblem 2

Set the factor '(-1 + o + -1n)' equal to zero and attempt to solve: Simplifying -1 + o + -1n = 0 Reorder the terms: -1 + -1n + o = 0 Solving -1 + -1n + o = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -1n + 1 + o = 0 + 1 Reorder the terms: -1 + 1 + -1n + o = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1n + o = 0 + 1 -1n + o = 0 + 1 Combine like terms: 0 + 1 = 1 -1n + o = 1 Add '-1o' to each side of the equation. -1n + o + -1o = 1 + -1o Combine like terms: o + -1o = 0 -1n + 0 = 1 + -1o -1n = 1 + -1o Divide each side by '-1'. n = -1 + o Simplifying n = -1 + o

Solution

n = {0, -1 + o}

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