4n(8n+2)+n(8n+8)=

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Solution for 4n(8n+2)+n(8n+8)= equation:


Simplifying
4n(8n + 2) + n(8n + 8) = 0

Reorder the terms:
4n(2 + 8n) + n(8n + 8) = 0
(2 * 4n + 8n * 4n) + n(8n + 8) = 0
(8n + 32n2) + n(8n + 8) = 0

Reorder the terms:
8n + 32n2 + n(8 + 8n) = 0
8n + 32n2 + (8 * n + 8n * n) = 0
8n + 32n2 + (8n + 8n2) = 0

Reorder the terms:
8n + 8n + 32n2 + 8n2 = 0

Combine like terms: 8n + 8n = 16n
16n + 32n2 + 8n2 = 0

Combine like terms: 32n2 + 8n2 = 40n2
16n + 40n2 = 0

Solving
16n + 40n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '8n'.
8n(2 + 5n) = 0

Ignore the factor 8.

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 '(2 + 5n)' equal to zero and attempt to solve: Simplifying 2 + 5n = 0 Solving 2 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5n = 0 + -2 5n = 0 + -2 Combine like terms: 0 + -2 = -2 5n = -2 Divide each side by '5'. n = -0.4 Simplifying n = -0.4

Solution

n = {0, -0.4}

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