0=x^2-22x+57

Solution for 0=x^2-22x+57 equation:

Simplifying
0 = x2 + -22x + 57

Reorder the terms:
0 = 57 + -22x + x2

Solving
0 = 57 + -22x + x2

Solving for variable 'x'.

Combine like terms: 0 + -57 = -57
-57 + 22x + -1x2 = 57 + -22x + x2 + -57 + 22x + -1x2

Reorder the terms:
-57 + 22x + -1x2 = 57 + -57 + -22x + 22x + x2 + -1x2

Combine like terms: 57 + -57 = 0
-57 + 22x + -1x2 = 0 + -22x + 22x + x2 + -1x2
-57 + 22x + -1x2 = -22x + 22x + x2 + -1x2

Combine like terms: -22x + 22x = 0
-57 + 22x + -1x2 = 0 + x2 + -1x2
-57 + 22x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-57 + 22x + -1x2 = 0

Factor a trinomial.
(-19 + x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-19 + x)' equal to zero and attempt to solve:

Simplifying
-19 + x = 0

Solving
-19 + x = 0

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

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

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

Combine like terms: 0 + 19 = 19
x = 19

Simplifying
x = 19
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {19, 3}