0=(r+4)(4r-8)

Solution for 0=(r+4)(4r-8) equation:

Simplifying
0 = (r + 4)(4r + -8)

Reorder the terms:
0 = (4 + r)(4r + -8)

Reorder the terms:
0 = (4 + r)(-8 + 4r)

Multiply (4 + r) * (-8 + 4r)
0 = (4(-8 + 4r) + r(-8 + 4r))
0 = ((-8 * 4 + 4r * 4) + r(-8 + 4r))
0 = ((-32 + 16r) + r(-8 + 4r))
0 = (-32 + 16r + (-8 * r + 4r * r))
0 = (-32 + 16r + (-8r + 4r2))

Combine like terms: 16r + -8r = 8r
0 = (-32 + 8r + 4r2)

Solving
0 = -32 + 8r + 4r2

Solving for variable 'r'.

Combine like terms: 0 + 32 = 32
32 + -8r + -4r2 = -32 + 8r + 4r2 + 32 + -8r + -4r2

Reorder the terms:
32 + -8r + -4r2 = -32 + 32 + 8r + -8r + 4r2 + -4r2

Combine like terms: -32 + 32 = 0
32 + -8r + -4r2 = 0 + 8r + -8r + 4r2 + -4r2
32 + -8r + -4r2 = 8r + -8r + 4r2 + -4r2

Combine like terms: 8r + -8r = 0
32 + -8r + -4r2 = 0 + 4r2 + -4r2
32 + -8r + -4r2 = 4r2 + -4r2

Combine like terms: 4r2 + -4r2 = 0
32 + -8r + -4r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + -2r + -1r2) = 0

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

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

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

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

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

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

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 0

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

Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4

Combine like terms: 0 + -4 = -4
r = -4

Simplifying
r = -4
Solution
r = {2, -4}