(5n-1)(n-5)=0

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


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

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

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

Multiply (-1 + 5n) * (-5 + n)
(-1(-5 + n) + 5n * (-5 + n)) = 0
((-5 * -1 + n * -1) + 5n * (-5 + n)) = 0
((5 + -1n) + 5n * (-5 + n)) = 0
(5 + -1n + (-5 * 5n + n * 5n)) = 0
(5 + -1n + (-25n + 5n2)) = 0

Combine like terms: -1n + -25n = -26n
(5 + -26n + 5n2) = 0

Solving
5 + -26n + 5n2 = 0

Solving for variable 'n'.

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

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 '(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 = {0.2, 5}

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