(5n-7)(n+8)=0

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Solution for (5n-7)(n+8)=0 equation: 


Simplifying
(5n + -7)(n + 8) = 0

Reorder the terms:
(-7 + 5n)(n + 8) = 0

Reorder the terms:
(-7 + 5n)(8 + n) = 0

Multiply (-7 + 5n) * (8 + n)
(-7(8 + n) + 5n * (8 + n)) = 0
((8 * -7 + n * -7) + 5n * (8 + n)) = 0
((-56 + -7n) + 5n * (8 + n)) = 0
(-56 + -7n + (8 * 5n + n * 5n)) = 0
(-56 + -7n + (40n + 5n2)) = 0

Combine like terms: -7n + 40n = 33n
(-56 + 33n + 5n2) = 0

Solving
-56 + 33n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-8 + -1n)(7 + -5n) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -5n)' equal to zero and attempt to solve:

Simplifying
7 + -5n = 0

Solving
7 + -5n = 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 + -5n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5n = 0 + -7
-5n = 0 + -7

Combine like terms: 0 + -7 = -7
-5n = -7

Divide each side by '-5'.
n = 1.4

Simplifying
n = 1.4
Solution
n = {-8, 1.4}

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