x^2-46x+205=0

Solution for x^2-46x+205=0 equation:

Simplifying
x2 + -46x + 205 = 0

Reorder the terms:
205 + -46x + x2 = 0

Solving
205 + -46x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(41 + -1x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(41 + -1x)' equal to zero and attempt to solve:

Simplifying
41 + -1x = 0

Solving
41 + -1x = 0

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

Add '-41' to each side of the equation.
41 + -41 + -1x = 0 + -41

Combine like terms: 41 + -41 = 0
0 + -1x = 0 + -41
-1x = 0 + -41

Combine like terms: 0 + -41 = -41
-1x = -41

Divide each side by '-1'.
x = 41

Simplifying
x = 41
Solution
x = {5, 41}