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

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


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

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

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

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

Combine like terms: -8n + 7n = -1n
(-56 + -1n + n2) = 0

Solving
-56 + -1n + n2 = 0

Solving for variable 'n'.

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


Subproblem 1
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

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 = {-7, 8}

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