(4r+1)(4r+4)=0

Solution for (4r+1)(4r+4)=0 equation:

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

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

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

Multiply (1 + 4r) * (4 + 4r)
(1(4 + 4r) + 4r * (4 + 4r)) = 0
((4 * 1 + 4r * 1) + 4r * (4 + 4r)) = 0
((4 + 4r) + 4r * (4 + 4r)) = 0
(4 + 4r + (4 * 4r + 4r * 4r)) = 0
(4 + 4r + (16r + 16r2)) = 0

Combine like terms: 4r + 16r = 20r
(4 + 20r + 16r2) = 0

Solving
4 + 20r + 16r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 5r + 4r2) = 0

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

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

Simplifying
1 + r = 0

Solving
1 + r = 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 + r = 0 + -1

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

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

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

Simplifying
1 + 4r = 0

Solving
1 + 4r = 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 + 4r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4r = 0 + -1
4r = 0 + -1

Combine like terms: 0 + -1 = -1
4r = -1

Divide each side by '4'.
r = -0.25

Simplifying
r = -0.25
Solution
r = {-1, -0.25}