=(2r+3)(3r+5)

Solution for =(2r+3)(3r+5) equation:

Simplifying
0 = (2r + 3)(3r + 5)

Reorder the terms:
0 = (3 + 2r)(3r + 5)

Reorder the terms:
0 = (3 + 2r)(5 + 3r)

Multiply (3 + 2r) * (5 + 3r)
0 = (3(5 + 3r) + 2r * (5 + 3r))
0 = ((5 * 3 + 3r * 3) + 2r * (5 + 3r))
0 = ((15 + 9r) + 2r * (5 + 3r))
0 = (15 + 9r + (5 * 2r + 3r * 2r))
0 = (15 + 9r + (10r + 6r2))

Combine like terms: 9r + 10r = 19r
0 = (15 + 19r + 6r2)

Solving
0 = 15 + 19r + 6r2

Solving for variable 'r'.

Combine like terms: 0 + -15 = -15
-15 + -19r + -6r2 = 15 + 19r + 6r2 + -15 + -19r + -6r2

Reorder the terms:
-15 + -19r + -6r2 = 15 + -15 + 19r + -19r + 6r2 + -6r2

Combine like terms: 15 + -15 = 0
-15 + -19r + -6r2 = 0 + 19r + -19r + 6r2 + -6r2
-15 + -19r + -6r2 = 19r + -19r + 6r2 + -6r2

Combine like terms: 19r + -19r = 0
-15 + -19r + -6r2 = 0 + 6r2 + -6r2
-15 + -19r + -6r2 = 6r2 + -6r2

Combine like terms: 6r2 + -6r2 = 0
-15 + -19r + -6r2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 19r + 6r2) = 0

Factor a trinomial.
-1((5 + 3r)(3 + 2r)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 3r)' equal to zero and attempt to solve:

Simplifying
5 + 3r = 0

Solving
5 + 3r = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3r = 0 + -5
3r = 0 + -5

Combine like terms: 0 + -5 = -5
3r = -5

Divide each side by '3'.
r = -1.666666667

Simplifying
r = -1.666666667
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 = {-1.666666667, -1.5}