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

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


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

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

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

Multiply (8 + 7n) * (-7 + 2n)
(8(-7 + 2n) + 7n * (-7 + 2n)) = 0
((-7 * 8 + 2n * 8) + 7n * (-7 + 2n)) = 0
((-56 + 16n) + 7n * (-7 + 2n)) = 0
(-56 + 16n + (-7 * 7n + 2n * 7n)) = 0
(-56 + 16n + (-49n + 14n2)) = 0

Combine like terms: 16n + -49n = -33n
(-56 + -33n + 14n2) = 0

Solving
-56 + -33n + 14n2 = 0

Solving for variable 'n'.

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


Subproblem 1
Set the factor '(-8 + -7n)' equal to zero and attempt to solve:

Simplifying
-8 + -7n = 0

Solving
-8 + -7n = 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 + -7n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7n = 0 + 8
-7n = 0 + 8

Combine like terms: 0 + 8 = 8
-7n = 8

Divide each side by '-7'.
n = -1.142857143

Simplifying
n = -1.142857143

Subproblem 2
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
Solution
n = {-1.142857143, 3.5}

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