n^2=10n+3000

Solution for n^2=10n+3000 equation:

Simplifying
n2 = 10n + 3000

Reorder the terms:
n2 = 3000 + 10n

Solving
n2 = 3000 + 10n

Solving for variable 'n'.

Reorder the terms:
-3000 + -10n + n2 = 3000 + 10n + -3000 + -10n

Reorder the terms:
-3000 + -10n + n2 = 3000 + -3000 + 10n + -10n

Combine like terms: 3000 + -3000 = 0
-3000 + -10n + n2 = 0 + 10n + -10n
-3000 + -10n + n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
-3000 + -10n + n2 = 0

Factor a trinomial.
(-50 + -1n)(60 + -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 '(60 + -1n)' equal to zero and attempt to solve:

Simplifying
60 + -1n = 0

Solving
60 + -1n = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1n = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1n = 0 + -60
-1n = 0 + -60

Combine like terms: 0 + -60 = -60
-1n = -60

Divide each side by '-1'.
n = 60

Simplifying
n = 60
Solution
n = {-50, 60}