=12n^2-67n+16

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Solution for =12n^2-67n+16 equation:


Simplifying
0 = 12n2 + -67n + 16

Reorder the terms:
0 = 16 + -67n + 12n2

Solving
0 = 16 + -67n + 12n2

Solving for variable 'n'.

Combine like terms: 0 + -16 = -16
-16 + 67n + -12n2 = 16 + -67n + 12n2 + -16 + 67n + -12n2

Reorder the terms:
-16 + 67n + -12n2 = 16 + -16 + -67n + 67n + 12n2 + -12n2

Combine like terms: 16 + -16 = 0
-16 + 67n + -12n2 = 0 + -67n + 67n + 12n2 + -12n2
-16 + 67n + -12n2 = -67n + 67n + 12n2 + -12n2

Combine like terms: -67n + 67n = 0
-16 + 67n + -12n2 = 0 + 12n2 + -12n2
-16 + 67n + -12n2 = 12n2 + -12n2

Combine like terms: 12n2 + -12n2 = 0
-16 + 67n + -12n2 = 0

Factor a trinomial.
(-16 + 3n)(1 + -4n) = 0

Subproblem 1

Set the factor '(-16 + 3n)' equal to zero and attempt to solve: Simplifying -16 + 3n = 0 Solving -16 + 3n = 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 + 3n = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 3n = 0 + 16 3n = 0 + 16 Combine like terms: 0 + 16 = 16 3n = 16 Divide each side by '3'. n = 5.333333333 Simplifying n = 5.333333333

Subproblem 2

Set the factor '(1 + -4n)' equal to zero and attempt to solve: Simplifying 1 + -4n = 0 Solving 1 + -4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4n = 0 + -1 -4n = 0 + -1 Combine like terms: 0 + -1 = -1 -4n = -1 Divide each side by '-4'. n = 0.25 Simplifying n = 0.25

Solution

n = {5.333333333, 0.25}

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