(n+50)(n-20)=0

Solution for (n+50)(n-20)=0 equation:

Simplifying
(n + 50)(n + -20) = 0

Reorder the terms:
(50 + n)(n + -20) = 0

Reorder the terms:
(50 + n)(-20 + n) = 0

Multiply (50 + n) * (-20 + n)
(50(-20 + n) + n(-20 + n)) = 0
((-20 * 50 + n * 50) + n(-20 + n)) = 0
((-1000 + 50n) + n(-20 + n)) = 0
(-1000 + 50n + (-20 * n + n * n)) = 0
(-1000 + 50n + (-20n + n2)) = 0

Combine like terms: 50n + -20n = 30n
(-1000 + 30n + n2) = 0

Solving
-1000 + 30n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-50 + -1n)(20 + -1n) = 0

Subproblem 1
Set the factor '(-50 + -1n)' equal to zero and attempt to solve:

Simplifying
-50 + -1n = 0

Solving
-50 + -1n = 0

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

Add '50' to each side of the equation.
-50 + 50 + -1n = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -1n = 0 + 50
-1n = 0 + 50

Combine like terms: 0 + 50 = 50
-1n = 50

Divide each side by '-1'.
n = -50

Simplifying
n = -50
Subproblem 2
Set the factor '(20 + -1n)' equal to zero and attempt to solve:

Simplifying
20 + -1n = 0

Solving
20 + -1n = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1n = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1n = 0 + -20
-1n = 0 + -20

Combine like terms: 0 + -20 = -20
-1n = -20

Divide each side by '-1'.
n = 20

Simplifying
n = 20
Solution
n = {-50, 20}