(5n-8)(n+2)=0

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Solution for (5n-8)(n+2)=0 equation:


Simplifying
(5n + -8)(n + 2) = 0

Reorder the terms:
(-8 + 5n)(n + 2) = 0

Reorder the terms:
(-8 + 5n)(2 + n) = 0

Multiply (-8 + 5n) * (2 + n)
(-8(2 + n) + 5n * (2 + n)) = 0
((2 * -8 + n * -8) + 5n * (2 + n)) = 0
((-16 + -8n) + 5n * (2 + n)) = 0
(-16 + -8n + (2 * 5n + n * 5n)) = 0
(-16 + -8n + (10n + 5n2)) = 0

Combine like terms: -8n + 10n = 2n
(-16 + 2n + 5n2) = 0

Solving
-16 + 2n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-2 + -1n)(8 + -5n) = 0

Subproblem 1

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

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 = {-2, 1.6}

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