12g^2-5g-3=0

Solution for 12g^2-5g-3=0 equation:

Simplifying
12g2 + -5g + -3 = 0

Reorder the terms:
-3 + -5g + 12g2 = 0

Solving
-3 + -5g + 12g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-1 + -3g)(3 + -4g) = 0

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

Simplifying
-1 + -3g = 0

Solving
-1 + -3g = 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 + -3g = 0 + 1

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

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

Divide each side by '-3'.
g = -0.3333333333

Simplifying
g = -0.3333333333
Subproblem 2
Set the factor '(3 + -4g)' equal to zero and attempt to solve:

Simplifying
3 + -4g = 0

Solving
3 + -4g = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4g = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4g = 0 + -3
-4g = 0 + -3

Combine like terms: 0 + -3 = -3
-4g = -3

Divide each side by '-4'.
g = 0.75

Simplifying
g = 0.75
Solution
g = {-0.3333333333, 0.75}