4r(r+4)=33

Solution for 4r(r+4)=33 equation:

Simplifying
4r(r + 4) = 33

Reorder the terms:
4r(4 + r) = 33
(4 * 4r + r * 4r) = 33
(16r + 4r2) = 33

Solving
16r + 4r2 = 33

Solving for variable 'r'.

Reorder the terms:
-33 + 16r + 4r2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + 16r + 4r2 = 0

Factor a trinomial.
(-11 + -2r)(3 + -2r) = 0

Subproblem 1
Set the factor '(-11 + -2r)' equal to zero and attempt to solve:

Simplifying
-11 + -2r = 0

Solving
-11 + -2r = 0

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

Add '11' to each side of the equation.
-11 + 11 + -2r = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2r = 0 + 11
-2r = 0 + 11

Combine like terms: 0 + 11 = 11
-2r = 11

Divide each side by '-2'.
r = -5.5

Simplifying
r = -5.5
Subproblem 2
Set the factor '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 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 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {-5.5, 1.5}