0=x^2-22x+105

Solution for 0=x^2-22x+105 equation:

Simplifying
0 = x2 + -22x + 105

Reorder the terms:
0 = 105 + -22x + x2

Solving
0 = 105 + -22x + x2

Solving for variable 'x'.

Combine like terms: 0 + -105 = -105
-105 + 22x + -1x2 = 105 + -22x + x2 + -105 + 22x + -1x2

Reorder the terms:
-105 + 22x + -1x2 = 105 + -105 + -22x + 22x + x2 + -1x2

Combine like terms: 105 + -105 = 0
-105 + 22x + -1x2 = 0 + -22x + 22x + x2 + -1x2
-105 + 22x + -1x2 = -22x + 22x + x2 + -1x2

Combine like terms: -22x + 22x = 0
-105 + 22x + -1x2 = 0 + x2 + -1x2
-105 + 22x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-105 + 22x + -1x2 = 0

Factor a trinomial.
(-15 + x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-15 + x)' equal to zero and attempt to solve:

Simplifying
-15 + x = 0

Solving
-15 + x = 0

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

Add '15' to each side of the equation.
-15 + 15 + x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + x = 0 + 15
x = 0 + 15

Combine like terms: 0 + 15 = 15
x = 15

Simplifying
x = 15
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {15, 7}