11(8r+3)2(9-6r)=

Solution for 11(8r+3)2(9-6r)= equation:

Simplifying
11(8r + 3) * 2(9 + -6r) = 0

Reorder the terms:
11(3 + 8r) * 2(9 + -6r) = 0

Reorder the terms for easier multiplication:
11 * 2(3 + 8r)(9 + -6r) = 0

Multiply 11 * 2
22(3 + 8r)(9 + -6r) = 0

Multiply (3 + 8r) * (9 + -6r)
22(3(9 + -6r) + 8r * (9 + -6r)) = 0
22((9 * 3 + -6r * 3) + 8r * (9 + -6r)) = 0
22((27 + -18r) + 8r * (9 + -6r)) = 0
22(27 + -18r + (9 * 8r + -6r * 8r)) = 0
22(27 + -18r + (72r + -48r2)) = 0

Combine like terms: -18r + 72r = 54r
22(27 + 54r + -48r2) = 0
(27 * 22 + 54r * 22 + -48r2 * 22) = 0
(594 + 1188r + -1056r2) = 0

Solving
594 + 1188r + -1056r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '66'.
66(9 + 18r + -16r2) = 0

Factor a trinomial.
66((3 + -2r)(3 + 8r)) = 0

Ignore the factor 66.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + 8r)' equal to zero and attempt to solve:

Simplifying
3 + 8r = 0

Solving
3 + 8r = 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 + 8r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8r = 0 + -3
8r = 0 + -3

Combine like terms: 0 + -3 = -3
8r = -3

Divide each side by '8'.
r = -0.375

Simplifying
r = -0.375
Solution
r = {1.5, -0.375}