0=x^2-20x+51

Solution for 0=x^2-20x+51 equation:

Simplifying
0 = x2 + -20x + 51

Reorder the terms:
0 = 51 + -20x + x2

Solving
0 = 51 + -20x + x2

Solving for variable 'x'.

Combine like terms: 0 + -51 = -51
-51 + 20x + -1x2 = 51 + -20x + x2 + -51 + 20x + -1x2

Reorder the terms:
-51 + 20x + -1x2 = 51 + -51 + -20x + 20x + x2 + -1x2

Combine like terms: 51 + -51 = 0
-51 + 20x + -1x2 = 0 + -20x + 20x + x2 + -1x2
-51 + 20x + -1x2 = -20x + 20x + x2 + -1x2

Combine like terms: -20x + 20x = 0
-51 + 20x + -1x2 = 0 + x2 + -1x2
-51 + 20x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-51 + 20x + -1x2 = 0

Factor a trinomial.
(-17 + x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-17 + x)' equal to zero and attempt to solve:

Simplifying
-17 + x = 0

Solving
-17 + x = 0

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

Add '17' to each side of the equation.
-17 + 17 + x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + x = 0 + 17
x = 0 + 17

Combine like terms: 0 + 17 = 17
x = 17

Simplifying
x = 17
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 = {17, 3}