(2r+1)(4r-4)=

Solution for (2r+1)(4r-4)= equation:

Simplifying
(2r + 1)(4r + -4) = 0

Reorder the terms:
(1 + 2r)(4r + -4) = 0

Reorder the terms:
(1 + 2r)(-4 + 4r) = 0

Multiply (1 + 2r) * (-4 + 4r)
(1(-4 + 4r) + 2r * (-4 + 4r)) = 0
((-4 * 1 + 4r * 1) + 2r * (-4 + 4r)) = 0
((-4 + 4r) + 2r * (-4 + 4r)) = 0
(-4 + 4r + (-4 * 2r + 4r * 2r)) = 0
(-4 + 4r + (-8r + 8r2)) = 0

Combine like terms: 4r + -8r = -4r
(-4 + -4r + 8r2) = 0

Solving
-4 + -4r + 8r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -1r + 2r2) = 0

Factor a trinomial.
4((-1 + -2r)(1 + -1r)) = 0

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

Simplifying
-1 + -2r = 0

Solving
-1 + -2r = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2r = 0 + 1
-2r = 0 + 1

Combine like terms: 0 + 1 = 1
-2r = 1

Divide each side by '-2'.
r = -0.5

Simplifying
r = -0.5
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

Simplifying
r = 1
Solution
r = {-0.5, 1}