4n^2-88n=-468

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Solution for 4n^2-88n=-468 equation:


Simplifying
4n2 + -88n = -468

Reorder the terms:
-88n + 4n2 = -468

Solving
-88n + 4n2 = -468

Solving for variable 'n'.

Reorder the terms:
468 + -88n + 4n2 = -468 + 468

Combine like terms: -468 + 468 = 0
468 + -88n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(117 + -22n + n2) = 0

Factor a trinomial.
4((9 + -1n)(13 + -1n)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9

Subproblem 2

Set the factor '(13 + -1n)' equal to zero and attempt to solve: Simplifying 13 + -1n = 0 Solving 13 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1n = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1n = 0 + -13 -1n = 0 + -13 Combine like terms: 0 + -13 = -13 -1n = -13 Divide each side by '-1'. n = 13 Simplifying n = 13

Solution

n = {9, 13}

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