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

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


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

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

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

Multiply (8 + 5n) * (-5 + n)
(8(-5 + n) + 5n * (-5 + n)) = 0
((-5 * 8 + n * 8) + 5n * (-5 + n)) = 0
((-40 + 8n) + 5n * (-5 + n)) = 0
(-40 + 8n + (-5 * 5n + n * 5n)) = 0
(-40 + 8n + (-25n + 5n2)) = 0

Combine like terms: 8n + -25n = -17n
(-40 + -17n + 5n2) = 0

Solving
-40 + -17n + 5n2 = 0

Solving for variable 'n'.

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

Subproblem 1

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

Subproblem 2

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

Solution

n = {-1.6, 5}

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