21n^2+112n-448=0

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Solution for 21n^2+112n-448=0 equation:


Simplifying
21n2 + 112n + -448 = 0

Reorder the terms:
-448 + 112n + 21n2 = 0

Solving
-448 + 112n + 21n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-64 + 16n + 3n2) = 0

Factor a trinomial.
7((-8 + -1n)(8 + -3n)) = 0

Ignore the factor 7.

Subproblem 1

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

Subproblem 2

Set the factor '(8 + -3n)' equal to zero and attempt to solve: Simplifying 8 + -3n = 0 Solving 8 + -3n = 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 + -3n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3n = 0 + -8 -3n = 0 + -8 Combine like terms: 0 + -8 = -8 -3n = -8 Divide each side by '-3'. n = 2.666666667 Simplifying n = 2.666666667

Solution

n = {-8, 2.666666667}

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