3n^2+96=36n

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Solution for 3n^2+96=36n equation:


Simplifying
3n2 + 96 = 36n

Reorder the terms:
96 + 3n2 = 36n

Solving
96 + 3n2 = 36n

Solving for variable 'n'.

Reorder the terms:
96 + -36n + 3n2 = 36n + -36n

Combine like terms: 36n + -36n = 0
96 + -36n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(32 + -12n + n2) = 0

Factor a trinomial.
3((4 + -1n)(8 + -1n)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4

Subproblem 2

Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8

Solution

n = {4, 8}

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