(2r+-3)(3r+4)=

Solution for (2r+-3)(3r+4)= equation:

Simplifying
(2r + -3)(3r + 4) = 0

Reorder the terms:
(-3 + 2r)(3r + 4) = 0

Reorder the terms:
(-3 + 2r)(4 + 3r) = 0

Multiply (-3 + 2r) * (4 + 3r)
(-3(4 + 3r) + 2r * (4 + 3r)) = 0
((4 * -3 + 3r * -3) + 2r * (4 + 3r)) = 0
((-12 + -9r) + 2r * (4 + 3r)) = 0
(-12 + -9r + (4 * 2r + 3r * 2r)) = 0
(-12 + -9r + (8r + 6r2)) = 0

Combine like terms: -9r + 8r = -1r
(-12 + -1r + 6r2) = 0

Solving
-12 + -1r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-4 + -3r)(3 + -2r) = 0

Subproblem 1
Set the factor '(-4 + -3r)' equal to zero and attempt to solve:

Simplifying
-4 + -3r = 0

Solving
-4 + -3r = 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 + -3r = 0 + 4

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

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

Divide each side by '-3'.
r = -1.333333333

Simplifying
r = -1.333333333
Subproblem 2
Set the factor '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 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 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {-1.333333333, 1.5}