4n^2-16n-21=44

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Solution for 4n^2-16n-21=44 equation:


Simplifying
4n2 + -16n + -21 = 44

Reorder the terms:
-21 + -16n + 4n2 = 44

Solving
-21 + -16n + 4n2 = 44

Solving for variable 'n'.

Reorder the terms:
-21 + -44 + -16n + 4n2 = 44 + -44

Combine like terms: -21 + -44 = -65
-65 + -16n + 4n2 = 44 + -44

Combine like terms: 44 + -44 = 0
-65 + -16n + 4n2 = 0

Factor a trinomial.
(-5 + -2n)(13 + -2n) = 0

Subproblem 1

Set the factor '(-5 + -2n)' equal to zero and attempt to solve: Simplifying -5 + -2n = 0 Solving -5 + -2n = 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 + -2n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2n = 0 + 5 -2n = 0 + 5 Combine like terms: 0 + 5 = 5 -2n = 5 Divide each side by '-2'. n = -2.5 Simplifying n = -2.5

Subproblem 2

Set the factor '(13 + -2n)' equal to zero and attempt to solve: Simplifying 13 + -2n = 0 Solving 13 + -2n = 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 + -2n = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2n = 0 + -13 -2n = 0 + -13 Combine like terms: 0 + -13 = -13 -2n = -13 Divide each side by '-2'. n = 6.5 Simplifying n = 6.5

Solution

n = {-2.5, 6.5}

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