(g^2)+(g-6)=0

Solution for (g^2)+(g-6)=0 equation:

Simplifying
(g2) + (g + -6) = 0
g2 + (g + -6) = 0

Reorder the terms:
g2 + (-6 + g) = 0

Remove parenthesis around (-6 + g)
g2 + -6 + g = 0

Reorder the terms:
-6 + g + g2 = 0

Solving
-6 + g + g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-3 + -1g)(2 + -1g) = 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 '(2 + -1g)' equal to zero and attempt to solve:

Simplifying
2 + -1g = 0

Solving
2 + -1g = 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 + -1g = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1g = 0 + -2
-1g = 0 + -2

Combine like terms: 0 + -2 = -2
-1g = -2

Divide each side by '-1'.
g = 2

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