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

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


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

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

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

Multiply (-5 + 2n) * (-8 + n)
(-5(-8 + n) + 2n * (-8 + n)) = 0
((-8 * -5 + n * -5) + 2n * (-8 + n)) = 0
((40 + -5n) + 2n * (-8 + n)) = 0
(40 + -5n + (-8 * 2n + n * 2n)) = 0
(40 + -5n + (-16n + 2n2)) = 0

Combine like terms: -5n + -16n = -21n
(40 + -21n + 2n2) = 0

Solving
40 + -21n + 2n2 = 0

Solving for variable 'n'.

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


Subproblem 1
Set the factor '(5 + -2n)' equal to zero and attempt to solve:

Simplifying
5 + -2n = 0

Solving
5 + -2n = 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 + -2n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2n = 0 + -5
-2n = 0 + -5

Combine like terms: 0 + -5 = -5
-2n = -5

Divide each side by '-2'.
n = 2.5

Simplifying
n = 2.5

Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 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 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {2.5, 8}

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