x^2-13x+53=17

Solution for x^2-13x+53=17 equation:

Simplifying
x2 + -13x + 53 = 17

Reorder the terms:
53 + -13x + x2 = 17

Solving
53 + -13x + x2 = 17

Solving for variable 'x'.

Reorder the terms:
53 + -17 + -13x + x2 = 17 + -17

Combine like terms: 53 + -17 = 36
36 + -13x + x2 = 17 + -17

Combine like terms: 17 + -17 = 0
36 + -13x + x2 = 0

Factor a trinomial.
(4 + -1x)(9 + -1x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {4, 9}