0=x^2-20x-224

Solution for 0=x^2-20x-224 equation:

Simplifying
0 = x2 + -20x + -224

Reorder the terms:
0 = -224 + -20x + x2

Solving
0 = -224 + -20x + x2

Solving for variable 'x'.

Combine like terms: 0 + 224 = 224
224 + 20x + -1x2 = -224 + -20x + x2 + 224 + 20x + -1x2

Reorder the terms:
224 + 20x + -1x2 = -224 + 224 + -20x + 20x + x2 + -1x2

Combine like terms: -224 + 224 = 0
224 + 20x + -1x2 = 0 + -20x + 20x + x2 + -1x2
224 + 20x + -1x2 = -20x + 20x + x2 + -1x2

Combine like terms: -20x + 20x = 0
224 + 20x + -1x2 = 0 + x2 + -1x2
224 + 20x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
224 + 20x + -1x2 = 0

Factor a trinomial.
(28 + -1x)(8 + x) = 0

Subproblem 1
Set the factor '(28 + -1x)' equal to zero and attempt to solve:

Simplifying
28 + -1x = 0

Solving
28 + -1x = 0

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

Add '-28' to each side of the equation.
28 + -28 + -1x = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -1x = 0 + -28
-1x = 0 + -28

Combine like terms: 0 + -28 = -28
-1x = -28

Divide each side by '-1'.
x = 28

Simplifying
x = 28
Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {28, -8}