(n-8)(2n-7)=0

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Solution for (n-8)(2n-7)=0 equation: 


Simplifying
(n + -8)(2n + -7) = 0

Reorder the terms:
(-8 + n)(2n + -7) = 0

Reorder the terms:
(-8 + n)(-7 + 2n) = 0

Multiply (-8 + n) * (-7 + 2n)
(-8(-7 + 2n) + n(-7 + 2n)) = 0
((-7 * -8 + 2n * -8) + n(-7 + 2n)) = 0
((56 + -16n) + n(-7 + 2n)) = 0
(56 + -16n + (-7 * n + 2n * n)) = 0
(56 + -16n + (-7n + 2n2)) = 0

Combine like terms: -16n + -7n = -23n
(56 + -23n + 2n2) = 0

Solving
56 + -23n + 2n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(7 + -2n)(8 + -1n) = 0


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

Simplifying
7 + -2n = 0

Solving
7 + -2n = 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 + -2n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2n = 0 + -7
-2n = 0 + -7

Combine like terms: 0 + -7 = -7
-2n = -7

Divide each side by '-2'.
n = 3.5

Simplifying
n = 3.5

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 = {3.5, 8}

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