5n^2+2n+14n=3n^2-4(5n)

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Solution for 5n^2+2n+14n=3n^2-4(5n) equation: 


Simplifying
5n2 + 2n + 14n = 3n2 + -4(5n)

Reorder the terms:
2n + 14n + 5n2 = 3n2 + -4(5n)

Combine like terms: 2n + 14n = 16n
16n + 5n2 = 3n2 + -4(5n)

Remove parenthesis around (5n)
16n + 5n2 = 3n2 + -4 * 5n

Multiply -4 * 5
16n + 5n2 = 3n2 + -20n

Reorder the terms:
16n + 5n2 = -20n + 3n2

Solving
16n + 5n2 = -20n + 3n2

Solving for variable 'n'.

Reorder the terms:
16n + 20n + 5n2 + -3n2 = -20n + 3n2 + 20n + -3n2

Combine like terms: 16n + 20n = 36n
36n + 5n2 + -3n2 = -20n + 3n2 + 20n + -3n2

Combine like terms: 5n2 + -3n2 = 2n2
36n + 2n2 = -20n + 3n2 + 20n + -3n2

Reorder the terms:
36n + 2n2 = -20n + 20n + 3n2 + -3n2

Combine like terms: -20n + 20n = 0
36n + 2n2 = 0 + 3n2 + -3n2
36n + 2n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
36n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2n'.
2n(18 + n) = 0

Ignore the factor 2.

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 '(18 + n)' equal to zero and attempt to solve:

Simplifying
18 + n = 0

Solving
18 + n = 0

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

Add '-18' to each side of the equation.
18 + -18 + n = 0 + -18

Combine like terms: 18 + -18 = 0
0 + n = 0 + -18
n = 0 + -18

Combine like terms: 0 + -18 = -18
n = -18

Simplifying
n = -18
Solution
n = {0, -18}

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