3n^2=24-n

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


Simplifying
3n2 = 24 + -1n

Solving
3n2 = 24 + -1n

Solving for variable 'n'.

Reorder the terms:
-24 + n + 3n2 = 24 + -1n + -24 + n

Reorder the terms:
-24 + n + 3n2 = 24 + -24 + -1n + n

Combine like terms: 24 + -24 = 0
-24 + n + 3n2 = 0 + -1n + n
-24 + n + 3n2 = -1n + n

Combine like terms: -1n + n = 0
-24 + n + 3n2 = 0

Factor a trinomial.
(-3 + -1n)(8 + -3n) = 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 '(8 + -3n)' equal to zero and attempt to solve: Simplifying 8 + -3n = 0 Solving 8 + -3n = 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 + -3n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3n = 0 + -8 -3n = 0 + -8 Combine like terms: 0 + -8 = -8 -3n = -8 Divide each side by '-3'. n = 2.666666667 Simplifying n = 2.666666667

Solution

n = {-3, 2.666666667}

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