8n^2+24n+10=0

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Solution for 8n^2+24n+10=0 equation:


Simplifying
8n2 + 24n + 10 = 0

Reorder the terms:
10 + 24n + 8n2 = 0

Solving
10 + 24n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 12n + 4n2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + 2n)' equal to zero and attempt to solve: Simplifying 5 + 2n = 0 Solving 5 + 2n = 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 + 2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2n = 0 + -5 2n = 0 + -5 Combine like terms: 0 + -5 = -5 2n = -5 Divide each side by '2'. n = -2.5 Simplifying n = -2.5

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 = {-2.5, -0.5}

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