r(r+4)=96

Solution for r(r+4)=96 equation:

Simplifying
r(r + 4) = 96

Reorder the terms:
r(4 + r) = 96
(4 * r + r * r) = 96
(4r + r2) = 96

Solving
4r + r2 = 96

Solving for variable 'r'.

Reorder the terms:
-96 + 4r + r2 = 96 + -96

Combine like terms: 96 + -96 = 0
-96 + 4r + r2 = 0

Factor a trinomial.
(-12 + -1r)(8 + -1r) = 0

Subproblem 1
Set the factor '(-12 + -1r)' equal to zero and attempt to solve:

Simplifying
-12 + -1r = 0

Solving
-12 + -1r = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1r = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1r = 0 + 12
-1r = 0 + 12

Combine like terms: 0 + 12 = 12
-1r = 12

Divide each side by '-1'.
r = -12

Simplifying
r = -12
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 = {-12, 8}