(-42+-1n)(10+-1n)=0

Solution for (-42+-1n)(10+-1n)=0 equation:

Simplifying
(-42 + -1n)(10 + -1n) = 0

Multiply (-42 + -1n) * (10 + -1n)
(-42(10 + -1n) + -1n * (10 + -1n)) = 0
((10 * -42 + -1n * -42) + -1n * (10 + -1n)) = 0
((-420 + 42n) + -1n * (10 + -1n)) = 0
(-420 + 42n + (10 * -1n + -1n * -1n)) = 0
(-420 + 42n + (-10n + 1n2)) = 0

Combine like terms: 42n + -10n = 32n
(-420 + 32n + 1n2) = 0

Solving
-420 + 32n + 1n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-42 + -1n)(10 + -1n) = 0

Subproblem 1
Set the factor '(-42 + -1n)' equal to zero and attempt to solve:

Simplifying
-42 + -1n = 0

Solving
-42 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '42' to each side of the equation.
-42 + 42 + -1n = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -1n = 0 + 42
-1n = 0 + 42

Combine like terms: 0 + 42 = 42
-1n = 42

Divide each side by '-1'.
n = -42

Simplifying
n = -42
Subproblem 2
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {-42, 10}