3n^2=-84-33n

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Solution for 3n^2=-84-33n equation:


Simplifying
3n2 = -84 + -33n

Solving
3n2 = -84 + -33n

Solving for variable 'n'.

Reorder the terms:
84 + 33n + 3n2 = -84 + -33n + 84 + 33n

Reorder the terms:
84 + 33n + 3n2 = -84 + 84 + -33n + 33n

Combine like terms: -84 + 84 = 0
84 + 33n + 3n2 = 0 + -33n + 33n
84 + 33n + 3n2 = -33n + 33n

Combine like terms: -33n + 33n = 0
84 + 33n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(28 + 11n + n2) = 0

Factor a trinomial.
3((7 + n)(4 + n)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(7 + n)' equal to zero and attempt to solve: Simplifying 7 + n = 0 Solving 7 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + n = 0 + -7 n = 0 + -7 Combine like terms: 0 + -7 = -7 n = -7 Simplifying n = -7

Subproblem 2

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

Solution

n = {-7, -4}

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