4n^2+16n+n=0

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Solution for 4n^2+16n+n=0 equation: 


Simplifying
4n2 + 16n + n = 0

Reorder the terms:
16n + n + 4n2 = 0

Combine like terms: 16n + n = 17n
17n + 4n2 = 0

Solving
17n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(17 + 4n) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

Move all terms containing n to the left, all other terms to the right.

Simplifying
n = 0

Subproblem 2
Set the factor '(17 + 4n)' equal to zero and attempt to solve:

Simplifying
17 + 4n = 0

Solving
17 + 4n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-17' to each side of the equation.
17 + -17 + 4n = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 4n = 0 + -17
4n = 0 + -17

Combine like terms: 0 + -17 = -17
4n = -17

Divide each side by '4'.
n = -4.25

Simplifying
n = -4.25
Solution
n = {0, -4.25}

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