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

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


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

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

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

Multiply (-7 + n) * (-7 + 8n)
7(-7(-7 + 8n) + n(-7 + 8n)) = 0
7((-7 * -7 + 8n * -7) + n(-7 + 8n)) = 0
7((49 + -56n) + n(-7 + 8n)) = 0
7(49 + -56n + (-7 * n + 8n * n)) = 0
7(49 + -56n + (-7n + 8n2)) = 0

Combine like terms: -56n + -7n = -63n
7(49 + -63n + 8n2) = 0
(49 * 7 + -63n * 7 + 8n2 * 7) = 0
(343 + -441n + 56n2) = 0

Solving
343 + -441n + 56n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '7'.
7(49 + -63n + 8n2) = 0

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

Ignore the factor 7.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 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 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {0.875, 7}

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