n(n-1)-90=0

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Solution for n(n-1)-90=0 equation:


Simplifying
n(n + -1) + -90 = 0

Reorder the terms:
n(-1 + n) + -90 = 0
(-1 * n + n * n) + -90 = 0
(-1n + n2) + -90 = 0

Reorder the terms:
-90 + -1n + n2 = 0

Solving
-90 + -1n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-9 + -1n)(10 + -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 '(10 + -1n)' equal to zero and attempt to solve: Simplifying 10 + -1n = 0 Solving 10 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1n = 0 + -10 -1n = 0 + -10 Combine like terms: 0 + -10 = -10 -1n = -10 Divide each side by '-1'. n = 10 Simplifying n = 10

Solution

n = {-9, 10}

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