(2g-1)(g+3)=0

Solution for (2g-1)(g+3)=0 equation:

Simplifying
(2g + -1)(g + 3) = 0

Reorder the terms:
(-1 + 2g)(g + 3) = 0

Reorder the terms:
(-1 + 2g)(3 + g) = 0

Multiply (-1 + 2g) * (3 + g)
(-1(3 + g) + 2g * (3 + g)) = 0
((3 * -1 + g * -1) + 2g * (3 + g)) = 0
((-3 + -1g) + 2g * (3 + g)) = 0
(-3 + -1g + (3 * 2g + g * 2g)) = 0
(-3 + -1g + (6g + 2g2)) = 0

Combine like terms: -1g + 6g = 5g
(-3 + 5g + 2g2) = 0

Solving
-3 + 5g + 2g2 = 0

Solving for variable 'g'.

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

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

Simplifying
-3 + -1g = 0

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

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

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

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

Simplifying
g = -3
Subproblem 2
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
Solution
g = {-3, 0.5}