5g^2+15g+10=0

Solution for 5g^2+15g+10=0 equation:

Simplifying
5g2 + 15g + 10 = 0

Reorder the terms:
10 + 15g + 5g2 = 0

Solving
10 + 15g + 5g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + 3g + g2) = 0

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

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

Simplifying
2 + g = 0

Solving
2 + g = 0

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

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

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

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

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

Simplifying
1 + g = 0

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

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

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

Simplifying
g = -1
Solution
g = {-2, -1}