7n^2-14n=336

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Solution for 7n^2-14n=336 equation:


Simplifying
7n2 + -14n = 336

Reorder the terms:
-14n + 7n2 = 336

Solving
-14n + 7n2 = 336

Solving for variable 'n'.

Reorder the terms:
-336 + -14n + 7n2 = 336 + -336

Combine like terms: 336 + -336 = 0
-336 + -14n + 7n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-48 + -2n + n2) = 0

Factor a trinomial.
7((-6 + -1n)(8 + -1n)) = 0

Ignore the factor 7.

Subproblem 1

Set the factor '(-6 + -1n)' equal to zero and attempt to solve: Simplifying -6 + -1n = 0 Solving -6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1n = 0 + 6 -1n = 0 + 6 Combine like terms: 0 + 6 = 6 -1n = 6 Divide each side by '-1'. n = -6 Simplifying n = -6

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 = {-6, 8}

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