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

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


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

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

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

Multiply (7 + 8n) * (-8 + 5n)
(7(-8 + 5n) + 8n * (-8 + 5n)) = 0
((-8 * 7 + 5n * 7) + 8n * (-8 + 5n)) = 0
((-56 + 35n) + 8n * (-8 + 5n)) = 0
(-56 + 35n + (-8 * 8n + 5n * 8n)) = 0
(-56 + 35n + (-64n + 40n2)) = 0

Combine like terms: 35n + -64n = -29n
(-56 + -29n + 40n2) = 0

Solving
-56 + -29n + 40n2 = 0

Solving for variable 'n'.

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


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 '(8 + -5n)' equal to zero and attempt to solve:

Simplifying
8 + -5n = 0

Solving
8 + -5n = 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 + -5n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5n = 0 + -8
-5n = 0 + -8

Combine like terms: 0 + -8 = -8
-5n = -8

Divide each side by '-5'.
n = 1.6

Simplifying
n = 1.6
Solution
n = {-0.875, 1.6}

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