x^2-52x+507=0

Solution for x^2-52x+507=0 equation:

Simplifying
x2 + -52x + 507 = 0

Reorder the terms:
507 + -52x + x2 = 0

Solving
507 + -52x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + -1x)(39 + -1x) = 0

Subproblem 1
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Subproblem 2
Set the factor '(39 + -1x)' equal to zero and attempt to solve:

Simplifying
39 + -1x = 0

Solving
39 + -1x = 0

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

Add '-39' to each side of the equation.
39 + -39 + -1x = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -1x = 0 + -39
-1x = 0 + -39

Combine like terms: 0 + -39 = -39
-1x = -39

Divide each side by '-1'.
x = 39

Simplifying
x = 39
Solution
x = {13, 39}