15n^2+10n-200=0

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Solution for 15n^2+10n-200=0 equation:


Simplifying
15n2 + 10n + -200 = 0

Reorder the terms:
-200 + 10n + 15n2 = 0

Solving
-200 + 10n + 15n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-40 + 2n + 3n2) = 0

Factor a trinomial.
5((-4 + -1n)(10 + -3n)) = 0

Ignore the factor 5.

Subproblem 1

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

Subproblem 2

Set the factor '(10 + -3n)' equal to zero and attempt to solve: Simplifying 10 + -3n = 0 Solving 10 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3n = 0 + -10 -3n = 0 + -10 Combine like terms: 0 + -10 = -10 -3n = -10 Divide each side by '-3'. n = 3.333333333 Simplifying n = 3.333333333

Solution

n = {-4, 3.333333333}

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