5n^2=n+48

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Solution for 5n^2=n+48 equation:


Simplifying
5n2 = n + 48

Reorder the terms:
5n2 = 48 + n

Solving
5n2 = 48 + n

Solving for variable 'n'.

Reorder the terms:
-48 + -1n + 5n2 = 48 + n + -48 + -1n

Reorder the terms:
-48 + -1n + 5n2 = 48 + -48 + n + -1n

Combine like terms: 48 + -48 = 0
-48 + -1n + 5n2 = 0 + n + -1n
-48 + -1n + 5n2 = n + -1n

Combine like terms: n + -1n = 0
-48 + -1n + 5n2 = 0

Factor a trinomial.
(-3 + -1n)(16 + -5n) = 0

Subproblem 1

Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3

Subproblem 2

Set the factor '(16 + -5n)' equal to zero and attempt to solve: Simplifying 16 + -5n = 0 Solving 16 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -5n = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -5n = 0 + -16 -5n = 0 + -16 Combine like terms: 0 + -16 = -16 -5n = -16 Divide each side by '-5'. n = 3.2 Simplifying n = 3.2

Solution

n = {-3, 3.2}

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