24n^2-92n-72=0

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Solution for 24n^2-92n-72=0 equation:


Simplifying
24n2 + -92n + -72 = 0

Reorder the terms:
-72 + -92n + 24n2 = 0

Solving
-72 + -92n + 24n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + -23n + 6n2) = 0

Factor a trinomial.
4((-2 + -3n)(9 + -2n)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-2 + -3n)' equal to zero and attempt to solve: Simplifying -2 + -3n = 0 Solving -2 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3n = 0 + 2 -3n = 0 + 2 Combine like terms: 0 + 2 = 2 -3n = 2 Divide each side by '-3'. n = -0.6666666667 Simplifying n = -0.6666666667

Subproblem 2

Set the factor '(9 + -2n)' equal to zero and attempt to solve: Simplifying 9 + -2n = 0 Solving 9 + -2n = 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 + -2n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2n = 0 + -9 -2n = 0 + -9 Combine like terms: 0 + -9 = -9 -2n = -9 Divide each side by '-2'. n = 4.5 Simplifying n = 4.5

Solution

n = {-0.6666666667, 4.5}

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