r^2-rg-30g^2=

Solution for r^2-rg-30g^2= equation:

Simplifying
r2 + -1rg + -30g2 = 0

Reorder the terms:
-1gr + -30g2 + r2 = 0

Solving
-1gr + -30g2 + r2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-5g + -1r)(6g + -1r) = 0

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

Simplifying
-5g + -1r = 0

Solving
-5g + -1r = 0

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

Add 'r' to each side of the equation.
-5g + -1r + r = 0 + r

Combine like terms: -1r + r = 0
-5g + 0 = 0 + r
-5g = 0 + r
Remove the zero:
-5g = r

Divide each side by '-5'.
g = -0.2r

Simplifying
g = -0.2r
Subproblem 2
Set the factor '(6g + -1r)' equal to zero and attempt to solve:

Simplifying
6g + -1r = 0

Solving
6g + -1r = 0

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

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

Combine like terms: -1r + r = 0
6g + 0 = 0 + r
6g = 0 + r
Remove the zero:
6g = r

Divide each side by '6'.
g = 0.1666666667r

Simplifying
g = 0.1666666667r
Solution
g = {-0.2r, 0.1666666667r}