=(2r+1)(3r-1)

Solution for =(2r+1)(3r-1) equation:

Simplifying
0 = (2r + 1)(3r + -1)

Reorder the terms:
0 = (1 + 2r)(3r + -1)

Reorder the terms:
0 = (1 + 2r)(-1 + 3r)

Multiply (1 + 2r) * (-1 + 3r)
0 = (1(-1 + 3r) + 2r * (-1 + 3r))
0 = ((-1 * 1 + 3r * 1) + 2r * (-1 + 3r))
0 = ((-1 + 3r) + 2r * (-1 + 3r))
0 = (-1 + 3r + (-1 * 2r + 3r * 2r))
0 = (-1 + 3r + (-2r + 6r2))

Combine like terms: 3r + -2r = 1r
0 = (-1 + 1r + 6r2)

Solving
0 = -1 + 1r + 6r2

Solving for variable 'r'.

Combine like terms: 0 + 1 = 1
1 + -1r + -6r2 = -1 + 1r + 6r2 + 1 + -1r + -6r2

Reorder the terms:
1 + -1r + -6r2 = -1 + 1 + 1r + -1r + 6r2 + -6r2

Combine like terms: -1 + 1 = 0
1 + -1r + -6r2 = 0 + 1r + -1r + 6r2 + -6r2
1 + -1r + -6r2 = 1r + -1r + 6r2 + -6r2

Combine like terms: 1r + -1r = 0
1 + -1r + -6r2 = 0 + 6r2 + -6r2
1 + -1r + -6r2 = 6r2 + -6r2

Combine like terms: 6r2 + -6r2 = 0
1 + -1r + -6r2 = 0

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

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

Simplifying
1 + -3r = 0

Solving
1 + -3r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3r = 0 + -1
-3r = 0 + -1

Combine like terms: 0 + -1 = -1
-3r = -1

Divide each side by '-3'.
r = 0.3333333333

Simplifying
r = 0.3333333333
Subproblem 2
Set the factor '(1 + 2r)' equal to zero and attempt to solve:

Simplifying
1 + 2r = 0

Solving
1 + 2r = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2r = 0 + -1
2r = 0 + -1

Combine like terms: 0 + -1 = -1
2r = -1

Divide each side by '2'.
r = -0.5

Simplifying
r = -0.5
Solution
r = {0.3333333333, -0.5}