4r^2-6r+2=0

Solution for 4r^2-6r+2=0 equation:

Simplifying
4r2 + -6r + 2 = 0

Reorder the terms:
2 + -6r + 4r2 = 0

Solving
2 + -6r + 4r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -3r + 2r2) = 0

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

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

Simplifying
1 + -1r = 0

Solving
1 + -1r = 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 + -1r = 0 + -1

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

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

Divide each side by '-1'.
r = 1

Simplifying
r = 1
Solution
r = {0.5, 1}