10n^2=-85n-175

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Solution for 10n^2=-85n-175 equation:


Simplifying
10n2 = -85n + -175

Reorder the terms:
10n2 = -175 + -85n

Solving
10n2 = -175 + -85n

Solving for variable 'n'.

Reorder the terms:
175 + 85n + 10n2 = -175 + -85n + 175 + 85n

Reorder the terms:
175 + 85n + 10n2 = -175 + 175 + -85n + 85n

Combine like terms: -175 + 175 = 0
175 + 85n + 10n2 = 0 + -85n + 85n
175 + 85n + 10n2 = -85n + 85n

Combine like terms: -85n + 85n = 0
175 + 85n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(35 + 17n + 2n2) = 0

Factor a trinomial.
5((5 + n)(7 + 2n)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 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 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5

Subproblem 2

Set the factor '(7 + 2n)' equal to zero and attempt to solve: Simplifying 7 + 2n = 0 Solving 7 + 2n = 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 + 2n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2n = 0 + -7 2n = 0 + -7 Combine like terms: 0 + -7 = -7 2n = -7 Divide each side by '2'. n = -3.5 Simplifying n = -3.5

Solution

n = {-5, -3.5}

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