n^2-n-45=65

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Solution for n^2-n-45=65 equation:


Simplifying
n2 + -1n + -45 = 65

Reorder the terms:
-45 + -1n + n2 = 65

Solving
-45 + -1n + n2 = 65

Solving for variable 'n'.

Reorder the terms:
-45 + -65 + -1n + n2 = 65 + -65

Combine like terms: -45 + -65 = -110
-110 + -1n + n2 = 65 + -65

Combine like terms: 65 + -65 = 0
-110 + -1n + n2 = 0

Factor a trinomial.
(-10 + -1n)(11 + -1n) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(11 + -1n)' equal to zero and attempt to solve: Simplifying 11 + -1n = 0 Solving 11 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1n = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1n = 0 + -11 -1n = 0 + -11 Combine like terms: 0 + -11 = -11 -1n = -11 Divide each side by '-1'. n = 11 Simplifying n = 11

Solution

n = {-10, 11}

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