n^2-n-8=-2

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Solution for n^2-n-8=-2 equation:


Simplifying
n2 + -1n + -8 = -2

Reorder the terms:
-8 + -1n + n2 = -2

Solving
-8 + -1n + n2 = -2

Solving for variable 'n'.

Reorder the terms:
-8 + 2 + -1n + n2 = -2 + 2

Combine like terms: -8 + 2 = -6
-6 + -1n + n2 = -2 + 2

Combine like terms: -2 + 2 = 0
-6 + -1n + n2 = 0

Factor a trinomial.
(-2 + -1n)(3 + -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 '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Divide each side by '-1'. n = 3 Simplifying n = 3

Solution

n = {-2, 3}

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