0=2n^2+11n+5

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Solution for 0=2n^2+11n+5 equation:


Simplifying
0 = 2n2 + 11n + 5

Reorder the terms:
0 = 5 + 11n + 2n2

Solving
0 = 5 + 11n + 2n2

Solving for variable 'n'.

Combine like terms: 0 + -5 = -5
-5 + -11n + -2n2 = 5 + 11n + 2n2 + -5 + -11n + -2n2

Reorder the terms:
-5 + -11n + -2n2 = 5 + -5 + 11n + -11n + 2n2 + -2n2

Combine like terms: 5 + -5 = 0
-5 + -11n + -2n2 = 0 + 11n + -11n + 2n2 + -2n2
-5 + -11n + -2n2 = 11n + -11n + 2n2 + -2n2

Combine like terms: 11n + -11n = 0
-5 + -11n + -2n2 = 0 + 2n2 + -2n2
-5 + -11n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-5 + -11n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 11n + 2n2) = 0

Factor a trinomial.
-1((5 + n)(1 + 2n)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5

Subproblem 2

Set the factor '(1 + 2n)' equal to zero and attempt to solve: Simplifying 1 + 2n = 0 Solving 1 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2n = 0 + -1 2n = 0 + -1 Combine like terms: 0 + -1 = -1 2n = -1 Divide each side by '2'. n = -0.5 Simplifying n = -0.5

Solution

n = {-5, -0.5}

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