(6r-2)(3r-2)=

Solution for (6r-2)(3r-2)= equation:

Simplifying
(6r + -2)(3r + -2) = 0

Reorder the terms:
(-2 + 6r)(3r + -2) = 0

Reorder the terms:
(-2 + 6r)(-2 + 3r) = 0

Multiply (-2 + 6r) * (-2 + 3r)
(-2(-2 + 3r) + 6r * (-2 + 3r)) = 0
((-2 * -2 + 3r * -2) + 6r * (-2 + 3r)) = 0
((4 + -6r) + 6r * (-2 + 3r)) = 0
(4 + -6r + (-2 * 6r + 3r * 6r)) = 0
(4 + -6r + (-12r + 18r2)) = 0

Combine like terms: -6r + -12r = -18r
(4 + -18r + 18r2) = 0

Solving
4 + -18r + 18r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -9r + 9r2) = 0

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

Ignore the factor 2.
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 '(2 + -3r)' equal to zero and attempt to solve:

Simplifying
2 + -3r = 0

Solving
2 + -3r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3r = 0 + -2

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

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

Divide each side by '-3'.
r = 0.6666666667

Simplifying
r = 0.6666666667
Solution
r = {0.3333333333, 0.6666666667}