s^2+6sg-27g^2=

Solution for s^2+6sg-27g^2= equation:

Simplifying
s2 + 6sg + -27g2 = 0

Reorder the terms:
6gs + -27g2 + s2 = 0

Solving
6gs + -27g2 + s2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-9g + -1s)(3g + -1s) = 0

Subproblem 1
Set the factor '(-9g + -1s)' equal to zero and attempt to solve:

Simplifying
-9g + -1s = 0

Solving
-9g + -1s = 0

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

Add 's' to each side of the equation.
-9g + -1s + s = 0 + s

Combine like terms: -1s + s = 0
-9g + 0 = 0 + s
-9g = 0 + s
Remove the zero:
-9g = s

Divide each side by '-9'.
g = -0.1111111111s

Simplifying
g = -0.1111111111s
Subproblem 2
Set the factor '(3g + -1s)' equal to zero and attempt to solve:

Simplifying
3g + -1s = 0

Solving
3g + -1s = 0

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

Add 's' to each side of the equation.
3g + -1s + s = 0 + s

Combine like terms: -1s + s = 0
3g + 0 = 0 + s
3g = 0 + s
Remove the zero:
3g = s

Divide each side by '3'.
g = 0.3333333333s

Simplifying
g = 0.3333333333s
Solution
g = {-0.1111111111s, 0.3333333333s}