n(4n-5)(3n+1)=0

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Solution for n(4n-5)(3n+1)=0 equation:


Simplifying
n(4n + -5)(3n + 1) = 0

Reorder the terms:
n(-5 + 4n)(3n + 1) = 0

Reorder the terms:
n(-5 + 4n)(1 + 3n) = 0

Multiply (-5 + 4n) * (1 + 3n)
n(-5(1 + 3n) + 4n * (1 + 3n)) = 0
n((1 * -5 + 3n * -5) + 4n * (1 + 3n)) = 0
n((-5 + -15n) + 4n * (1 + 3n)) = 0
n(-5 + -15n + (1 * 4n + 3n * 4n)) = 0
n(-5 + -15n + (4n + 12n2)) = 0

Combine like terms: -15n + 4n = -11n
n(-5 + -11n + 12n2) = 0
(-5 * n + -11n * n + 12n2 * n) = 0
(-5n + -11n2 + 12n3) = 0

Solving
-5n + -11n2 + 12n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(-5 + -11n + 12n2) = 0

Factor a trinomial.
n((-1 + -3n)(5 + -4n)) = 0

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0

Subproblem 2

Set the factor '(-1 + -3n)' equal to zero and attempt to solve: Simplifying -1 + -3n = 0 Solving -1 + -3n = 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 + -3n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3n = 0 + 1 -3n = 0 + 1 Combine like terms: 0 + 1 = 1 -3n = 1 Divide each side by '-3'. n = -0.3333333333 Simplifying n = -0.3333333333

Subproblem 3

Set the factor '(5 + -4n)' equal to zero and attempt to solve: Simplifying 5 + -4n = 0 Solving 5 + -4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4n = 0 + -5 -4n = 0 + -5 Combine like terms: 0 + -5 = -5 -4n = -5 Divide each side by '-4'. n = 1.25 Simplifying n = 1.25

Solution

n = {0, -0.3333333333, 1.25}

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