x^2-90x+1001=0

Solution for x^2-90x+1001=0 equation:

Simplifying
x2 + -90x + 1001 = 0

Reorder the terms:
1001 + -90x + x2 = 0

Solving
1001 + -90x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + -1x)(77 + -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 '(77 + -1x)' equal to zero and attempt to solve:

Simplifying
77 + -1x = 0

Solving
77 + -1x = 0

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

Add '-77' to each side of the equation.
77 + -77 + -1x = 0 + -77

Combine like terms: 77 + -77 = 0
0 + -1x = 0 + -77
-1x = 0 + -77

Combine like terms: 0 + -77 = -77
-1x = -77

Divide each side by '-1'.
x = 77

Simplifying
x = 77
Solution
x = {13, 77}