2R^2-12R+18=0

Solution for 2R^2-12R+18=0 equation:

Simplifying
2R2 + -12R + 18 = 0

Reorder the terms:
18 + -12R + 2R2 = 0

Solving
18 + -12R + 2R2 = 0

Solving for variable 'R'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -6R + R2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1R)' equal to zero and attempt to solve:

Simplifying
3 + -1R = 0

Solving
3 + -1R = 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 + -1R = 0 + -3

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

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

Divide each side by '-1'.
R = 3

Simplifying
R = 3
Subproblem 2
Set the factor '(3 + -1R)' equal to zero and attempt to solve:

Simplifying
3 + -1R = 0

Solving
3 + -1R = 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 + -1R = 0 + -3

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

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

Divide each side by '-1'.
R = 3

Simplifying
R = 3
Solution
R = {3, 3}