3n^2+8=-14n

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Solution for 3n^2+8=-14n equation:


Simplifying
3n2 + 8 = -14n

Reorder the terms:
8 + 3n2 = -14n

Solving
8 + 3n2 = -14n

Solving for variable 'n'.

Reorder the terms:
8 + 14n + 3n2 = -14n + 14n

Combine like terms: -14n + 14n = 0
8 + 14n + 3n2 = 0

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

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 + 3n)' equal to zero and attempt to solve: Simplifying 2 + 3n = 0 Solving 2 + 3n = 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 + 3n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3n = 0 + -2 3n = 0 + -2 Combine like terms: 0 + -2 = -2 3n = -2 Divide each side by '3'. n = -0.6666666667 Simplifying n = -0.6666666667

Solution

n = {-4, -0.6666666667}

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