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

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

Simplifying
-4(r + 2) = 4r(2 + -4r)

Reorder the terms:
-4(2 + r) = 4r(2 + -4r)
(2 * -4 + r * -4) = 4r(2 + -4r)
(-8 + -4r) = 4r(2 + -4r)
-8 + -4r = (2 * 4r + -4r * 4r)
-8 + -4r = (8r + -16r2)

Solving
-8 + -4r = 8r + -16r2

Solving for variable 'r'.

Combine like terms: -4r + -8r = -12r
-8 + -12r + 16r2 = 8r + -16r2 + -8r + 16r2

Reorder the terms:
-8 + -12r + 16r2 = 8r + -8r + -16r2 + 16r2

Combine like terms: 8r + -8r = 0
-8 + -12r + 16r2 = 0 + -16r2 + 16r2
-8 + -12r + 16r2 = -16r2 + 16r2

Combine like terms: -16r2 + 16r2 = 0
-8 + -12r + 16r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -3r + 4r2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + -3r + 4r2)' equal to zero and attempt to solve:

Simplifying
-2 + -3r + 4r2 = 0

Solving
-2 + -3r + 4r2 = 0

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

Divide each side by '4'.
-0.5 + -0.75r + r2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.75r + 0.5 + r2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.75r + r2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.75r + r2 = 0 + 0.5
-0.75r + r2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.75r + r2 = 0.5

The r term is -0.75r.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75r + 0.140625 + r2 = 0.5 + 0.140625

Reorder the terms:
0.140625 + -0.75r + r2 = 0.5 + 0.140625

Combine like terms: 0.5 + 0.140625 = 0.640625
0.140625 + -0.75r + r2 = 0.640625

Factor a perfect square on the left side:
(r + -0.375)(r + -0.375) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(r + -0.375) equal to 0.80039053 and -0.80039053.

Subproblem 1
r + -0.375 = 0.80039053

Simplifying
r + -0.375 = 0.80039053

Reorder the terms:
-0.375 + r = 0.80039053

Solving
-0.375 + r = 0.80039053

Solving for variable 'r'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + r = 0.80039053 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + r = 0.80039053 + 0.375
r = 0.80039053 + 0.375

Combine like terms: 0.80039053 + 0.375 = 1.17539053
r = 1.17539053

Simplifying
r = 1.17539053

Subproblem 2
r + -0.375 = -0.80039053

Simplifying
r + -0.375 = -0.80039053

Reorder the terms:
-0.375 + r = -0.80039053

Solving
-0.375 + r = -0.80039053

Solving for variable 'r'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + r = -0.80039053 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + r = -0.80039053 + 0.375
r = -0.80039053 + 0.375

Combine like terms: -0.80039053 + 0.375 = -0.42539053
r = -0.42539053

Simplifying
r = -0.42539053

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.17539053, -0.42539053}
Solution
r = {1.17539053, -0.42539053}