-10n=n^2+25

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Solution for -10n=n^2+25 equation:


Simplifying
-10n = n2 + 25

Reorder the terms:
-10n = 25 + n2

Solving
-10n = 25 + n2

Solving for variable 'n'.

Reorder the terms:
-25 + -10n + -1n2 = 25 + n2 + -25 + -1n2

Reorder the terms:
-25 + -10n + -1n2 = 25 + -25 + n2 + -1n2

Combine like terms: 25 + -25 = 0
-25 + -10n + -1n2 = 0 + n2 + -1n2
-25 + -10n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-25 + -10n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(25 + 10n + n2) = 0

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

Ignore the factor -1.

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 '(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

Solution

n = {-5, -5}

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