(n^2)+(20n)=300

Solution for (n^2)+(20n)=300 equation:

Simplifying
(n2) + (20n) = 300
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.
(-30 + -1n)(10 + -1n) = 0

Subproblem 1
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
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 = {-30, 10}