r^2-20r-224=0

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

Simplifying
r2 + -20r + -224 = 0

Reorder the terms:
-224 + -20r + r2 = 0

Solving
-224 + -20r + r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(-8 + -1r)' equal to zero and attempt to solve:

Simplifying
-8 + -1r = 0

Solving
-8 + -1r = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1r = 0 + 8
-1r = 0 + 8

Combine like terms: 0 + 8 = 8
-1r = 8

Divide each side by '-1'.
r = -8

Simplifying
r = -8
Subproblem 2
Set the factor '(28 + -1r)' equal to zero and attempt to solve:

Simplifying
28 + -1r = 0

Solving
28 + -1r = 0

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

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

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

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

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

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