3n^2+18n+14=-10

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Solution for 3n^2+18n+14=-10 equation:


Simplifying
3n2 + 18n + 14 = -10

Reorder the terms:
14 + 18n + 3n2 = -10

Solving
14 + 18n + 3n2 = -10

Solving for variable 'n'.

Reorder the terms:
14 + 10 + 18n + 3n2 = -10 + 10

Combine like terms: 14 + 10 = 24
24 + 18n + 3n2 = -10 + 10

Combine like terms: -10 + 10 = 0
24 + 18n + 3n2 = 0

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

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

Ignore the factor 3.

Subproblem 1

Set the factor '(4 + n)' equal to zero and attempt to solve: Simplifying 4 + n = 0 Solving 4 + n = 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 + n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + n = 0 + -4 n = 0 + -4 Combine like terms: 0 + -4 = -4 n = -4 Simplifying n = -4

Subproblem 2

Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 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 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2

Solution

n = {-4, -2}

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