418=n^2-3n

Solution for 418=n^2-3n equation:

Simplifying
418 = n2 + -3n

Reorder the terms:
418 = -3n + n2

Solving
418 = -3n + n2

Solving for variable 'n'.

Reorder the terms:
418 + 3n + -1n2 = -3n + 3n + n2 + -1n2

Combine like terms: -3n + 3n = 0
418 + 3n + -1n2 = 0 + n2 + -1n2
418 + 3n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
418 + 3n + -1n2 = 0

Factor a trinomial.
(22 + -1n)(19 + n) = 0

Subproblem 1
Set the factor '(22 + -1n)' equal to zero and attempt to solve:

Simplifying
22 + -1n = 0

Solving
22 + -1n = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1n = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1n = 0 + -22
-1n = 0 + -22

Combine like terms: 0 + -22 = -22
-1n = -22

Divide each side by '-1'.
n = 22

Simplifying
n = 22
Subproblem 2
Set the factor '(19 + n)' equal to zero and attempt to solve:

Simplifying
19 + n = 0

Solving
19 + n = 0

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

Add '-19' to each side of the equation.
19 + -19 + n = 0 + -19

Combine like terms: 19 + -19 = 0
0 + n = 0 + -19
n = 0 + -19

Combine like terms: 0 + -19 = -19
n = -19

Simplifying
n = -19
Solution
n = {22, -19}