(6n-1)(8n-7)=0

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Solution for (6n-1)(8n-7)=0 equation: 


Simplifying
(6n + -1)(8n + -7) = 0

Reorder the terms:
(-1 + 6n)(8n + -7) = 0

Reorder the terms:
(-1 + 6n)(-7 + 8n) = 0

Multiply (-1 + 6n) * (-7 + 8n)
(-1(-7 + 8n) + 6n * (-7 + 8n)) = 0
((-7 * -1 + 8n * -1) + 6n * (-7 + 8n)) = 0
((7 + -8n) + 6n * (-7 + 8n)) = 0
(7 + -8n + (-7 * 6n + 8n * 6n)) = 0
(7 + -8n + (-42n + 48n2)) = 0

Combine like terms: -8n + -42n = -50n
(7 + -50n + 48n2) = 0

Solving
7 + -50n + 48n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + -6n)(7 + -8n) = 0


Subproblem 1
Set the factor '(1 + -6n)' equal to zero and attempt to solve:

Simplifying
1 + -6n = 0

Solving
1 + -6n = 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 + -6n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6n = 0 + -1
-6n = 0 + -1

Combine like terms: 0 + -1 = -1
-6n = -1

Divide each side by '-6'.
n = 0.1666666667

Simplifying
n = 0.1666666667

Subproblem 2
Set the factor '(7 + -8n)' equal to zero and attempt to solve:

Simplifying
7 + -8n = 0

Solving
7 + -8n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -8n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8n = 0 + -7
-8n = 0 + -7

Combine like terms: 0 + -7 = -7
-8n = -7

Divide each side by '-8'.
n = 0.875

Simplifying
n = 0.875
Solution
n = {0.1666666667, 0.875}

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