15n^2-27n=6

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Solution for 15n^2-27n=6 equation:


Simplifying
15n2 + -27n = 6

Reorder the terms:
-27n + 15n2 = 6

Solving
-27n + 15n2 = 6

Solving for variable 'n'.

Reorder the terms:
-6 + -27n + 15n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -27n + 15n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -9n + 5n2) = 0

Factor a trinomial.
3((-1 + -5n)(2 + -1n)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-1 + -5n)' equal to zero and attempt to solve: Simplifying -1 + -5n = 0 Solving -1 + -5n = 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 + -5n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5n = 0 + 1 -5n = 0 + 1 Combine like terms: 0 + 1 = 1 -5n = 1 Divide each side by '-5'. n = -0.2 Simplifying n = -0.2

Subproblem 2

Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 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 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2

Solution

n = {-0.2, 2}

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