243g^2+54g+3=0

Solution for 243g^2+54g+3=0 equation:

Simplifying
243g2 + 54g + 3 = 0

Reorder the terms:
3 + 54g + 243g2 = 0

Solving
3 + 54g + 243g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 18g + 81g2) = 0

Factor a trinomial.
3((1 + 9g)(1 + 9g)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + 9g)' equal to zero and attempt to solve:

Simplifying
1 + 9g = 0

Solving
1 + 9g = 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 + 9g = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9g = 0 + -1
9g = 0 + -1

Combine like terms: 0 + -1 = -1
9g = -1

Divide each side by '9'.
g = -0.1111111111

Simplifying
g = -0.1111111111
Subproblem 2
Set the factor '(1 + 9g)' equal to zero and attempt to solve:

Simplifying
1 + 9g = 0

Solving
1 + 9g = 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 + 9g = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9g = 0 + -1
9g = 0 + -1

Combine like terms: 0 + -1 = -1
9g = -1

Divide each side by '9'.
g = -0.1111111111

Simplifying
g = -0.1111111111
Solution
g = {-0.1111111111, -0.1111111111}