(4r+3)(r+1)=0

Solution for (4r+3)(r+1)=0 equation:

Simplifying
(4r + 3)(r + 1) = 0

Reorder the terms:
(3 + 4r)(r + 1) = 0

Reorder the terms:
(3 + 4r)(1 + r) = 0

Multiply (3 + 4r) * (1 + r)
(3(1 + r) + 4r * (1 + r)) = 0
((1 * 3 + r * 3) + 4r * (1 + r)) = 0
((3 + 3r) + 4r * (1 + r)) = 0
(3 + 3r + (1 * 4r + r * 4r)) = 0
(3 + 3r + (4r + 4r2)) = 0

Combine like terms: 3r + 4r = 7r
(3 + 7r + 4r2) = 0

Solving
3 + 7r + 4r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + r)(3 + 4r) = 0

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 '(3 + 4r)' equal to zero and attempt to solve:

Simplifying
3 + 4r = 0

Solving
3 + 4r = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4r = 0 + -3
4r = 0 + -3

Combine like terms: 0 + -3 = -3
4r = -3

Divide each side by '4'.
r = -0.75

Simplifying
r = -0.75
Solution
r = {-1, -0.75}