12n-n^2=35

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Solution for 12n-n^2=35 equation:


Simplifying
12n + -1n2 = 35

Solving
12n + -1n2 = 35

Solving for variable 'n'.

Reorder the terms:
-35 + 12n + -1n2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + 12n + -1n2 = 0

Factor a trinomial.
(-7 + n)(5 + -1n) = 0

Subproblem 1

Set the factor '(-7 + n)' equal to zero and attempt to solve: Simplifying -7 + n = 0 Solving -7 + n = 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 + n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + n = 0 + 7 n = 0 + 7 Combine like terms: 0 + 7 = 7 n = 7 Simplifying n = 7

Subproblem 2

Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5

Solution

n = {7, 5}

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