2g^2-3g-5=0

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

Simplifying
2g2 + -3g + -5 = 0

Reorder the terms:
-5 + -3g + 2g2 = 0

Solving
-5 + -3g + 2g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-1 + -1g)(5 + -2g) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -2g)' equal to zero and attempt to solve:

Simplifying
5 + -2g = 0

Solving
5 + -2g = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2g = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2g = 0 + -5
-2g = 0 + -5

Combine like terms: 0 + -5 = -5
-2g = -5

Divide each side by '-2'.
g = 2.5

Simplifying
g = 2.5
Solution
g = {-1, 2.5}