27-n^2=6n

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Solution for 27-n^2=6n equation:


Simplifying
27 + -1n2 = 6n

Solving
27 + -1n2 = 6n

Solving for variable 'n'.

Reorder the terms:
27 + -6n + -1n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
27 + -6n + -1n2 = 0

Factor a trinomial.
(3 + -1n)(9 + n) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(9 + n)' equal to zero and attempt to solve: Simplifying 9 + n = 0 Solving 9 + n = 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 + n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + n = 0 + -9 n = 0 + -9 Combine like terms: 0 + -9 = -9 n = -9 Simplifying n = -9

Solution

n = {3, -9}

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