r(r-4)=32

Solution for r(r-4)=32 equation:

Simplifying
r(r + -4) = 32

Reorder the terms:
r(-4 + r) = 32
(-4 * r + r * r) = 32
(-4r + r2) = 32

Solving
-4r + r2 = 32

Solving for variable 'r'.

Reorder the terms:
-32 + -4r + r2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + -4r + r2 = 0

Factor a trinomial.
(-4 + -1r)(8 + -1r) = 0

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 '(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
Solution
r = {-4, 8}