8n^2=24n+320

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Solution for 8n^2=24n+320 equation:


Simplifying
8n2 = 24n + 320

Reorder the terms:
8n2 = 320 + 24n

Solving
8n2 = 320 + 24n

Solving for variable 'n'.

Reorder the terms:
-320 + -24n + 8n2 = 320 + 24n + -320 + -24n

Reorder the terms:
-320 + -24n + 8n2 = 320 + -320 + 24n + -24n

Combine like terms: 320 + -320 = 0
-320 + -24n + 8n2 = 0 + 24n + -24n
-320 + -24n + 8n2 = 24n + -24n

Combine like terms: 24n + -24n = 0
-320 + -24n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-40 + -3n + n2) = 0

Factor a trinomial.
8((-5 + -1n)(8 + -1n)) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(-5 + -1n)' equal to zero and attempt to solve: Simplifying -5 + -1n = 0 Solving -5 + -1n = 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 + -1n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1n = 0 + 5 -1n = 0 + 5 Combine like terms: 0 + 5 = 5 -1n = 5 Divide each side by '-1'. n = -5 Simplifying n = -5

Subproblem 2

Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8

Solution

n = {-5, 8}

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