(9r+4)(r+3)=0

Solution for (9r+4)(r+3)=0 equation:

Simplifying
(9r + 4)(r + 3) = 0

Reorder the terms:
(4 + 9r)(r + 3) = 0

Reorder the terms:
(4 + 9r)(3 + r) = 0

Multiply (4 + 9r) * (3 + r)
(4(3 + r) + 9r * (3 + r)) = 0
((3 * 4 + r * 4) + 9r * (3 + r)) = 0
((12 + 4r) + 9r * (3 + r)) = 0
(12 + 4r + (3 * 9r + r * 9r)) = 0
(12 + 4r + (27r + 9r2)) = 0

Combine like terms: 4r + 27r = 31r
(12 + 31r + 9r2) = 0

Solving
12 + 31r + 9r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + r)(4 + 9r) = 0

Subproblem 1
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 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 + r = 0 + -3

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

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

Simplifying
r = -3
Subproblem 2
Set the factor '(4 + 9r)' equal to zero and attempt to solve:

Simplifying
4 + 9r = 0

Solving
4 + 9r = 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 + 9r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 9r = 0 + -4
9r = 0 + -4

Combine like terms: 0 + -4 = -4
9r = -4

Divide each side by '9'.
r = -0.4444444444

Simplifying
r = -0.4444444444
Solution
r = {-3, -0.4444444444}