4n^2-42n+80=0

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Solution for 4n^2-42n+80=0 equation:


Simplifying
4n2 + -42n + 80 = 0

Reorder the terms:
80 + -42n + 4n2 = 0

Solving
80 + -42n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + -21n + 2n2) = 0

Factor a trinomial.
2((5 + -2n)(8 + -1n)) = 0

Ignore the factor 2.

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 '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8

Solution

n = {2.5, 8}

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