3n^2=-24+18n

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Solution for 3n^2=-24+18n equation:


Simplifying
3n2 = -24 + 18n

Solving
3n2 = -24 + 18n

Solving for variable 'n'.

Reorder the terms:
24 + -18n + 3n2 = -24 + 18n + 24 + -18n

Reorder the terms:
24 + -18n + 3n2 = -24 + 24 + 18n + -18n

Combine like terms: -24 + 24 = 0
24 + -18n + 3n2 = 0 + 18n + -18n
24 + -18n + 3n2 = 18n + -18n

Combine like terms: 18n + -18n = 0
24 + -18n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -6n + n2) = 0

Factor a trinomial.
3((2 + -1n)(4 + -1n)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2

Subproblem 2

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

Solution

n = {2, 4}

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