5n(n+6)=-5n

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Solution for 5n(n+6)=-5n equation:


Simplifying
5n(n + 6) = -5n

Reorder the terms:
5n(6 + n) = -5n
(6 * 5n + n * 5n) = -5n
(30n + 5n2) = -5n

Solving
30n + 5n2 = -5n

Solving for variable 'n'.

Reorder the terms:
30n + 5n + 5n2 = -5n + 5n

Combine like terms: 30n + 5n = 35n
35n + 5n2 = -5n + 5n

Combine like terms: -5n + 5n = 0
35n + 5n2 = 0

Factor out the Greatest Common Factor (GCF), '5n'.
5n(7 + n) = 0

Ignore the factor 5.

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 '(7 + n)' equal to zero and attempt to solve: Simplifying 7 + n = 0 Solving 7 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + n = 0 + -7 n = 0 + -7 Combine like terms: 0 + -7 = -7 n = -7 Simplifying n = -7

Solution

n = {0, -7}

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