4n^2+16=-16n

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Solution for 4n^2+16=-16n equation:


Simplifying
4n2 + 16 = -16n

Reorder the terms:
16 + 4n2 = -16n

Solving
16 + 4n2 = -16n

Solving for variable 'n'.

Reorder the terms:
16 + 16n + 4n2 = -16n + 16n

Combine like terms: -16n + 16n = 0
16 + 16n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + 4n + n2) = 0

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

Ignore the factor 4.

Subproblem 1

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

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 = {-2, -2}

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