n^2-20n=300

Solution for n^2-20n=300 equation:

Simplifying
n2 + -20n = 300

Reorder the terms:
-20n + n2 = 300

Solving
-20n + n2 = 300

Solving for variable 'n'.

Reorder the terms:
-300 + -20n + n2 = 300 + -300

Combine like terms: 300 + -300 = 0
-300 + -20n + n2 = 0

Factor a trinomial.
(-10 + -1n)(30 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(30 + -1n)' equal to zero and attempt to solve:

Simplifying
30 + -1n = 0

Solving
30 + -1n = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1n = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1n = 0 + -30
-1n = 0 + -30

Combine like terms: 0 + -30 = -30
-1n = -30

Divide each side by '-1'.
n = 30

Simplifying
n = 30
Solution
n = {-10, 30}