21=r(r-4)

Solution for 21=r(r-4) equation:

Simplifying
21 = r(r + -4)

Reorder the terms:
21 = r(-4 + r)
21 = (-4 * r + r * r)
21 = (-4r + r2)

Solving
21 = -4r + r2

Solving for variable 'r'.

Reorder the terms:
21 + 4r + -1r2 = -4r + 4r + r2 + -1r2

Combine like terms: -4r + 4r = 0
21 + 4r + -1r2 = 0 + r2 + -1r2
21 + 4r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
21 + 4r + -1r2 = 0

Factor a trinomial.
(7 + -1r)(3 + r) = 0

Subproblem 1
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Subproblem 2
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 0

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

Add '-3' to each side of the equation.
3 + -3 + r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3

Combine like terms: 0 + -3 = -3
r = -3

Simplifying
r = -3
Solution
r = {7, -3}