3(25n^2-20n-32)=0

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Solution for 3(25n^2-20n-32)=0 equation:


Simplifying
3(25n2 + -20n + -32) = 0

Reorder the terms:
3(-32 + -20n + 25n2) = 0
(-32 * 3 + -20n * 3 + 25n2 * 3) = 0
(-96 + -60n + 75n2) = 0

Solving
-96 + -60n + 75n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-32 + -20n + 25n2) = 0

Factor a trinomial.
3((-4 + -5n)(8 + -5n)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-4 + -5n)' equal to zero and attempt to solve: Simplifying -4 + -5n = 0 Solving -4 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5n = 0 + 4 -5n = 0 + 4 Combine like terms: 0 + 4 = 4 -5n = 4 Divide each side by '-5'. n = -0.8 Simplifying n = -0.8

Subproblem 2

Set the factor '(8 + -5n)' equal to zero and attempt to solve: Simplifying 8 + -5n = 0 Solving 8 + -5n = 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 + -5n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5n = 0 + -8 -5n = 0 + -8 Combine like terms: 0 + -8 = -8 -5n = -8 Divide each side by '-5'. n = 1.6 Simplifying n = 1.6

Solution

n = {-0.8, 1.6}

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