5N(N-1)=N+8

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Solution for 5N(N-1)=N+8 equation:


Simplifying
5N(N + -1) = N + 8

Reorder the terms:
5N(-1 + N) = N + 8
(-1 * 5N + N * 5N) = N + 8
(-5N + 5N2) = N + 8

Reorder the terms:
-5N + 5N2 = 8 + N

Solving
-5N + 5N2 = 8 + N

Solving for variable 'N'.

Reorder the terms:
-8 + -5N + -1N + 5N2 = 8 + N + -8 + -1N

Combine like terms: -5N + -1N = -6N
-8 + -6N + 5N2 = 8 + N + -8 + -1N

Reorder the terms:
-8 + -6N + 5N2 = 8 + -8 + N + -1N

Combine like terms: 8 + -8 = 0
-8 + -6N + 5N2 = 0 + N + -1N
-8 + -6N + 5N2 = N + -1N

Combine like terms: N + -1N = 0
-8 + -6N + 5N2 = 0

Factor a trinomial.
(-4 + -5N)(2 + -1N) = 0

Subproblem 1

Set the factor '(-4 + -5N)' equal to zero and attempt to solve: Simplifying -4 + -5N = 0 Solving -4 + -5N = 0 Move all terms containing N to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5N = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5N = 0 + 4 -5N = 0 + 4 Combine like terms: 0 + 4 = 4 -5N = 4 Divide each side by '-5'. N = -0.8 Simplifying N = -0.8

Subproblem 2

Set the factor '(2 + -1N)' equal to zero and attempt to solve: Simplifying 2 + -1N = 0 Solving 2 + -1N = 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 + -1N = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1N = 0 + -2 -1N = 0 + -2 Combine like terms: 0 + -2 = -2 -1N = -2 Divide each side by '-1'. N = 2 Simplifying N = 2

Solution

N = {-0.8, 2}

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