(3r-7)(2r+3)=0

Solution for (3r-7)(2r+3)=0 equation:

Simplifying
(3r + -7)(2r + 3) = 0

Reorder the terms:
(-7 + 3r)(2r + 3) = 0

Reorder the terms:
(-7 + 3r)(3 + 2r) = 0

Multiply (-7 + 3r) * (3 + 2r)
(-7(3 + 2r) + 3r * (3 + 2r)) = 0
((3 * -7 + 2r * -7) + 3r * (3 + 2r)) = 0
((-21 + -14r) + 3r * (3 + 2r)) = 0
(-21 + -14r + (3 * 3r + 2r * 3r)) = 0
(-21 + -14r + (9r + 6r2)) = 0

Combine like terms: -14r + 9r = -5r
(-21 + -5r + 6r2) = 0

Solving
-21 + -5r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-3 + -2r)(7 + -3r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -3r)' equal to zero and attempt to solve:

Simplifying
7 + -3r = 0

Solving
7 + -3r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3r = 0 + -7
-3r = 0 + -7

Combine like terms: 0 + -7 = -7
-3r = -7

Divide each side by '-3'.
r = 2.333333333

Simplifying
r = 2.333333333
Solution
r = {-1.5, 2.333333333}