(8n-16)(5n-12)=0

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Solution for (8n-16)(5n-12)=0 equation: 


Simplifying
(8n + -16)(5n + -12) = 0

Reorder the terms:
(-16 + 8n)(5n + -12) = 0

Reorder the terms:
(-16 + 8n)(-12 + 5n) = 0

Multiply (-16 + 8n) * (-12 + 5n)
(-16(-12 + 5n) + 8n * (-12 + 5n)) = 0
((-12 * -16 + 5n * -16) + 8n * (-12 + 5n)) = 0
((192 + -80n) + 8n * (-12 + 5n)) = 0
(192 + -80n + (-12 * 8n + 5n * 8n)) = 0
(192 + -80n + (-96n + 40n2)) = 0

Combine like terms: -80n + -96n = -176n
(192 + -176n + 40n2) = 0

Solving
192 + -176n + 40n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '8'.
8(24 + -22n + 5n2) = 0

Factor a trinomial.
8((2 + -1n)(12 + -5n)) = 0

Ignore the factor 8.

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 '(12 + -5n)' equal to zero and attempt to solve:

Simplifying
12 + -5n = 0

Solving
12 + -5n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + -5n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -5n = 0 + -12
-5n = 0 + -12

Combine like terms: 0 + -12 = -12
-5n = -12

Divide each side by '-5'.
n = 2.4

Simplifying
n = 2.4
Solution
n = {2, 2.4}

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