(8n-1)(-3n-7)=0

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Solution for (8n-1)(-3n-7)=0 equation: 


Simplifying
(8n + -1)(-3n + -7) = 0

Reorder the terms:
(-1 + 8n)(-3n + -7) = 0

Reorder the terms:
(-1 + 8n)(-7 + -3n) = 0

Multiply (-1 + 8n) * (-7 + -3n)
(-1(-7 + -3n) + 8n * (-7 + -3n)) = 0
((-7 * -1 + -3n * -1) + 8n * (-7 + -3n)) = 0
((7 + 3n) + 8n * (-7 + -3n)) = 0
(7 + 3n + (-7 * 8n + -3n * 8n)) = 0
(7 + 3n + (-56n + -24n2)) = 0

Combine like terms: 3n + -56n = -53n
(7 + -53n + -24n2) = 0

Solving
7 + -53n + -24n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + -8n)(7 + 3n) = 0


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

Simplifying
1 + -8n = 0

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

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

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

Divide each side by '-8'.
n = 0.125

Simplifying
n = 0.125

Subproblem 2
Set the factor '(7 + 3n)' equal to zero and attempt to solve:

Simplifying
7 + 3n = 0

Solving
7 + 3n = 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 + 3n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3n = 0 + -7
3n = 0 + -7

Combine like terms: 0 + -7 = -7
3n = -7

Divide each side by '3'.
n = -2.333333333

Simplifying
n = -2.333333333
Solution
n = {0.125, -2.333333333}

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