-2r(5-r)=13+r

Solution for -2r(5-r)=13+r equation:

Simplifying
-2r(5 + -1r) = 13 + r
(5 * -2r + -1r * -2r) = 13 + r
(-10r + 2r2) = 13 + r

Solving
-10r + 2r2 = 13 + r

Solving for variable 'r'.

Reorder the terms:
-13 + -10r + -1r + 2r2 = 13 + r + -13 + -1r

Combine like terms: -10r + -1r = -11r
-13 + -11r + 2r2 = 13 + r + -13 + -1r

Reorder the terms:
-13 + -11r + 2r2 = 13 + -13 + r + -1r

Combine like terms: 13 + -13 = 0
-13 + -11r + 2r2 = 0 + r + -1r
-13 + -11r + 2r2 = r + -1r

Combine like terms: r + -1r = 0
-13 + -11r + 2r2 = 0

Factor a trinomial.
(-1 + -1r)(13 + -2r) = 0

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

Simplifying
-1 + -1r = 0

Solving
-1 + -1r = 0

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

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

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

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

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

Simplifying
r = -1
Subproblem 2
Set the factor '(13 + -2r)' equal to zero and attempt to solve:

Simplifying
13 + -2r = 0

Solving
13 + -2r = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2r = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2r = 0 + -13
-2r = 0 + -13

Combine like terms: 0 + -13 = -13
-2r = -13

Divide each side by '-2'.
r = 6.5

Simplifying
r = 6.5
Solution
r = {-1, 6.5}