6g^2-9g+3=0

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

Simplifying
6g2 + -9g + 3 = 0

Reorder the terms:
3 + -9g + 6g2 = 0

Solving
3 + -9g + 6g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -3g + 2g2) = 0

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

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

Simplifying
1 + -2g = 0

Solving
1 + -2g = 0

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

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

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

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

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

Simplifying
g = 0.5
Subproblem 2
Set the factor '(1 + -1g)' equal to zero and attempt to solve:

Simplifying
1 + -1g = 0

Solving
1 + -1g = 0

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

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

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

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

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

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