n^2-150n+5000=0

Solution for n^2-150n+5000=0 equation:

Simplifying
n2 + -150n + 5000 = 0

Reorder the terms:
5000 + -150n + n2 = 0

Solving
5000 + -150n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(50 + -1n)(100 + -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 '(100 + -1n)' equal to zero and attempt to solve:

Simplifying
100 + -1n = 0

Solving
100 + -1n = 0

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

Add '-100' to each side of the equation.
100 + -100 + -1n = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -1n = 0 + -100
-1n = 0 + -100

Combine like terms: 0 + -100 = -100
-1n = -100

Divide each side by '-1'.
n = 100

Simplifying
n = 100
Solution
n = {50, 100}