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

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

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

Reorder the terms:
g(6 + g) + -2(g + 6) = 0
(6 * g + g * g) + -2(g + 6) = 0
(6g + g2) + -2(g + 6) = 0

Reorder the terms:
6g + g2 + -2(6 + g) = 0
6g + g2 + (6 * -2 + g * -2) = 0
6g + g2 + (-12 + -2g) = 0

Reorder the terms:
-12 + 6g + -2g + g2 = 0

Combine like terms: 6g + -2g = 4g
-12 + 4g + g2 = 0

Solving
-12 + 4g + g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-6 + -1g)(2 + -1g) = 0

Subproblem 1
Set the factor '(-6 + -1g)' equal to zero and attempt to solve:

Simplifying
-6 + -1g = 0

Solving
-6 + -1g = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1g = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1g = 0 + 6
-1g = 0 + 6

Combine like terms: 0 + 6 = 6
-1g = 6

Divide each side by '-1'.
g = -6

Simplifying
g = -6
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 = {-6, 2}