n^2-91=6n

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Solution for n^2-91=6n equation:


Simplifying
n2 + -91 = 6n

Reorder the terms:
-91 + n2 = 6n

Solving
-91 + n2 = 6n

Solving for variable 'n'.

Reorder the terms:
-91 + -6n + n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
-91 + -6n + n2 = 0

Factor a trinomial.
(-7 + -1n)(13 + -1n) = 0

Subproblem 1

Set the factor '(-7 + -1n)' equal to zero and attempt to solve: Simplifying -7 + -1n = 0 Solving -7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1n = 0 + 7 -1n = 0 + 7 Combine like terms: 0 + 7 = 7 -1n = 7 Divide each side by '-1'. n = -7 Simplifying n = -7

Subproblem 2

Set the factor '(13 + -1n)' equal to zero and attempt to solve: Simplifying 13 + -1n = 0 Solving 13 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1n = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1n = 0 + -13 -1n = 0 + -13 Combine like terms: 0 + -13 = -13 -1n = -13 Divide each side by '-1'. n = 13 Simplifying n = 13

Solution

n = {-7, 13}

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