5n^2=100-5n

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Solution for 5n^2=100-5n equation:


Simplifying
5n2 = 100 + -5n

Solving
5n2 = 100 + -5n

Solving for variable 'n'.

Reorder the terms:
-100 + 5n + 5n2 = 100 + -5n + -100 + 5n

Reorder the terms:
-100 + 5n + 5n2 = 100 + -100 + -5n + 5n

Combine like terms: 100 + -100 = 0
-100 + 5n + 5n2 = 0 + -5n + 5n
-100 + 5n + 5n2 = -5n + 5n

Combine like terms: -5n + 5n = 0
-100 + 5n + 5n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-20 + n + n2) = 0

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

Ignore the factor 5.

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 '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 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 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4

Solution

n = {-5, 4}

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