112=20r+2r^2

Solution for 112=20r+2r^2 equation:

Simplifying
112 = 20r + 2r2

Solving
112 = 20r + 2r2

Solving for variable 'r'.

Reorder the terms:
112 + -20r + -2r2 = 20r + -20r + 2r2 + -2r2

Combine like terms: 20r + -20r = 0
112 + -20r + -2r2 = 0 + 2r2 + -2r2
112 + -20r + -2r2 = 2r2 + -2r2

Combine like terms: 2r2 + -2r2 = 0
112 + -20r + -2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(56 + -10r + -1r2) = 0

Factor a trinomial.
2((4 + -1r)(14 + r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Subproblem 2
Set the factor '(14 + r)' equal to zero and attempt to solve:

Simplifying
14 + r = 0

Solving
14 + r = 0

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

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

Combine like terms: 14 + -14 = 0
0 + r = 0 + -14
r = 0 + -14

Combine like terms: 0 + -14 = -14
r = -14

Simplifying
r = -14
Solution
r = {4, -14}