-24+2n^2=3n^2+11n

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Solution for -24+2n^2=3n^2+11n equation:


Simplifying
-24 + 2n2 = 3n2 + 11n

Reorder the terms:
-24 + 2n2 = 11n + 3n2

Solving
-24 + 2n2 = 11n + 3n2

Solving for variable 'n'.

Reorder the terms:
-24 + -11n + 2n2 + -3n2 = 11n + 3n2 + -11n + -3n2

Combine like terms: 2n2 + -3n2 = -1n2
-24 + -11n + -1n2 = 11n + 3n2 + -11n + -3n2

Reorder the terms:
-24 + -11n + -1n2 = 11n + -11n + 3n2 + -3n2

Combine like terms: 11n + -11n = 0
-24 + -11n + -1n2 = 0 + 3n2 + -3n2
-24 + -11n + -1n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
-24 + -11n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(24 + 11n + n2) = 0

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

Ignore the factor -1.

Subproblem 1

Set the factor '(8 + n)' equal to zero and attempt to solve: Simplifying 8 + n = 0 Solving 8 + n = 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 + n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + n = 0 + -8 n = 0 + -8 Combine like terms: 0 + -8 = -8 n = -8 Simplifying n = -8

Subproblem 2

Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 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 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3

Solution

n = {-8, -3}

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