2n^2+4n+1=337

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Solution for 2n^2+4n+1=337 equation:


Simplifying
2n2 + 4n + 1 = 337

Reorder the terms:
1 + 4n + 2n2 = 337

Solving
1 + 4n + 2n2 = 337

Solving for variable 'n'.

Reorder the terms:
1 + -337 + 4n + 2n2 = 337 + -337

Combine like terms: 1 + -337 = -336
-336 + 4n + 2n2 = 337 + -337

Combine like terms: 337 + -337 = 0
-336 + 4n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-168 + 2n + n2) = 0

Factor a trinomial.
2((-14 + -1n)(12 + -1n)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-14 + -1n)' equal to zero and attempt to solve: Simplifying -14 + -1n = 0 Solving -14 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1n = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1n = 0 + 14 -1n = 0 + 14 Combine like terms: 0 + 14 = 14 -1n = 14 Divide each side by '-1'. n = -14 Simplifying n = -14

Subproblem 2

Set the factor '(12 + -1n)' equal to zero and attempt to solve: Simplifying 12 + -1n = 0 Solving 12 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1n = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1n = 0 + -12 -1n = 0 + -12 Combine like terms: 0 + -12 = -12 -1n = -12 Divide each side by '-1'. n = 12 Simplifying n = 12

Solution

n = {-14, 12}

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