(4r+3)(3r+10)=0

Solution for (4r+3)(3r+10)=0 equation:

Simplifying
(4r + 3)(3r + 10) = 0

Reorder the terms:
(3 + 4r)(3r + 10) = 0

Reorder the terms:
(3 + 4r)(10 + 3r) = 0

Multiply (3 + 4r) * (10 + 3r)
(3(10 + 3r) + 4r * (10 + 3r)) = 0
((10 * 3 + 3r * 3) + 4r * (10 + 3r)) = 0
((30 + 9r) + 4r * (10 + 3r)) = 0
(30 + 9r + (10 * 4r + 3r * 4r)) = 0
(30 + 9r + (40r + 12r2)) = 0

Combine like terms: 9r + 40r = 49r
(30 + 49r + 12r2) = 0

Solving
30 + 49r + 12r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(10 + 3r)(3 + 4r) = 0

Subproblem 1
Set the factor '(10 + 3r)' equal to zero and attempt to solve:

Simplifying
10 + 3r = 0

Solving
10 + 3r = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3r = 0 + -10
3r = 0 + -10

Combine like terms: 0 + -10 = -10
3r = -10

Divide each side by '3'.
r = -3.333333333

Simplifying
r = -3.333333333
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 = {-3.333333333, -0.75}