(-3r)4(r+2)=11

Solution for (-3r)4(r+2)=11 equation:

Simplifying
(-3r) * 4(r + 2) = 11

Remove parenthesis around (-3r)
-3r * 4(r + 2) = 11

Reorder the terms:
-3r * 4(2 + r) = 11

Reorder the terms for easier multiplication:
-3 * 4r(2 + r) = 11

Multiply -3 * 4
-12r(2 + r) = 11
(2 * -12r + r * -12r) = 11
(-24r + -12r2) = 11

Solving
-24r + -12r2 = 11

Solving for variable 'r'.

Reorder the terms:
-11 + -24r + -12r2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -24r + -12r2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(11 + 24r + 12r2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(11 + 24r + 12r2)' equal to zero and attempt to solve:

Simplifying
11 + 24r + 12r2 = 0

Solving
11 + 24r + 12r2 = 0

Begin completing the square.  Divide all terms by
12 the coefficient of the squared term: 

Divide each side by '12'.
0.9166666667 + 2r + r2 = 0

Move the constant term to the right:

Add '-0.9166666667' to each side of the equation.
0.9166666667 + 2r + -0.9166666667 + r2 = 0 + -0.9166666667

Reorder the terms:
0.9166666667 + -0.9166666667 + 2r + r2 = 0 + -0.9166666667

Combine like terms: 0.9166666667 + -0.9166666667 = 0.0000000000
0.0000000000 + 2r + r2 = 0 + -0.9166666667
2r + r2 = 0 + -0.9166666667

Combine like terms: 0 + -0.9166666667 = -0.9166666667
2r + r2 = -0.9166666667

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = -0.9166666667 + 1

Reorder the terms:
1 + 2r + r2 = -0.9166666667 + 1

Combine like terms: -0.9166666667 + 1 = 0.0833333333
1 + 2r + r2 = 0.0833333333

Factor a perfect square on the left side:
(r + 1)(r + 1) = 0.0833333333

Calculate the square root of the right side: 0.288675135

Break this problem into two subproblems by setting 
(r + 1) equal to 0.288675135 and -0.288675135.

Subproblem 1
r + 1 = 0.288675135

Simplifying
r + 1 = 0.288675135

Reorder the terms:
1 + r = 0.288675135

Solving
1 + r = 0.288675135

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + -1 + r = 0.288675135 + -1

Combine like terms: 1 + -1 = 0
0 + r = 0.288675135 + -1
r = 0.288675135 + -1

Combine like terms: 0.288675135 + -1 = -0.711324865
r = -0.711324865

Simplifying
r = -0.711324865

Subproblem 2
r + 1 = -0.288675135

Simplifying
r + 1 = -0.288675135

Reorder the terms:
1 + r = -0.288675135

Solving
1 + r = -0.288675135

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + -1 + r = -0.288675135 + -1

Combine like terms: 1 + -1 = 0
0 + r = -0.288675135 + -1
r = -0.288675135 + -1

Combine like terms: -0.288675135 + -1 = -1.288675135
r = -1.288675135

Simplifying
r = -1.288675135

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.711324865, -1.288675135}
Solution
r = {-0.711324865, -1.288675135}