0=x^2-37x+322

Solution for 0=x^2-37x+322 equation:

Simplifying
0 = x2 + -37x + 322

Reorder the terms:
0 = 322 + -37x + x2

Solving
0 = 322 + -37x + x2

Solving for variable 'x'.

Combine like terms: 0 + -322 = -322
-322 + 37x + -1x2 = 322 + -37x + x2 + -322 + 37x + -1x2

Reorder the terms:
-322 + 37x + -1x2 = 322 + -322 + -37x + 37x + x2 + -1x2

Combine like terms: 322 + -322 = 0
-322 + 37x + -1x2 = 0 + -37x + 37x + x2 + -1x2
-322 + 37x + -1x2 = -37x + 37x + x2 + -1x2

Combine like terms: -37x + 37x = 0
-322 + 37x + -1x2 = 0 + x2 + -1x2
-322 + 37x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-322 + 37x + -1x2 = 0

Factor a trinomial.
(-23 + x)(14 + -1x) = 0

Subproblem 1
Set the factor '(-23 + x)' equal to zero and attempt to solve:

Simplifying
-23 + x = 0

Solving
-23 + x = 0

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

Add '23' to each side of the equation.
-23 + 23 + x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + x = 0 + 23
x = 0 + 23

Combine like terms: 0 + 23 = 23
x = 23

Simplifying
x = 23
Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {23, 14}