0=n(120-n)-50n

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Solution for 0=n(120-n)-50n equation:


Simplifying
0 = n(120 + -1n) + -50n
0 = (120 * n + -1n * n) + -50n
0 = (120n + -1n2) + -50n

Reorder the terms:
0 = 120n + -50n + -1n2

Combine like terms: 120n + -50n = 70n
0 = 70n + -1n2

Solving
0 = 70n + -1n2

Solving for variable 'n'.
Remove the zero:
-70n + n2 = 70n + -1n2 + -70n + n2

Reorder the terms:
-70n + n2 = 70n + -70n + -1n2 + n2

Combine like terms: 70n + -70n = 0
-70n + n2 = 0 + -1n2 + n2
-70n + n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
-70n + n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-70 + n) = 0

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 '(-70 + n)' equal to zero and attempt to solve: Simplifying -70 + n = 0 Solving -70 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + n = 0 + 70 Combine like terms: -70 + 70 = 0 0 + n = 0 + 70 n = 0 + 70 Combine like terms: 0 + 70 = 70 n = 70 Simplifying n = 70

Solution

n = {0, 70}

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