3d^2-9d+6=0

Solution for 3d^2-9d+6=0 equation:

Simplifying
3d2 + -9d + 6 = 0

Reorder the terms:
6 + -9d + 3d2 = 0

Solving
6 + -9d + 3d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -3d + d2) = 0

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

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

Simplifying
1 + -1d = 0

Solving
1 + -1d = 0

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

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

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

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

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

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

Simplifying
2 + -1d = 0

Solving
2 + -1d = 0

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

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

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

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

Divide each side by '-1'.
d = 2

Simplifying
d = 2
Solution
d = {1, 2}