2g^2+7g-15=0

Solution for 2g^2+7g-15=0 equation:

Simplifying
2g2 + 7g + -15 = 0

Reorder the terms:
-15 + 7g + 2g2 = 0

Solving
-15 + 7g + 2g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-5 + -1g)(3 + -2g) = 0

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

Simplifying
-5 + -1g = 0

Solving
-5 + -1g = 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 + -1g = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1g = 0 + 5
-1g = 0 + 5

Combine like terms: 0 + 5 = 5
-1g = 5

Divide each side by '-1'.
g = -5

Simplifying
g = -5
Subproblem 2
Set the factor '(3 + -2g)' equal to zero and attempt to solve:

Simplifying
3 + -2g = 0

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

Combine like terms: 3 + -3 = 0
0 + -2g = 0 + -3
-2g = 0 + -3

Combine like terms: 0 + -3 = -3
-2g = -3

Divide each side by '-2'.
g = 1.5

Simplifying
g = 1.5
Solution
g = {-5, 1.5}