r^2-4rg-21g^2=

Solution for r^2-4rg-21g^2= equation:

Simplifying
r2 + -4rg + -21g2 = 0

Reorder the terms:
-4gr + -21g2 + r2 = 0

Solving
-4gr + -21g2 + r2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-3g + -1r)(7g + -1r) = 0

Subproblem 1
Set the factor '(-3g + -1r)' equal to zero and attempt to solve:

Simplifying
-3g + -1r = 0

Solving
-3g + -1r = 0

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

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

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

Divide each side by '-3'.
g = -0.3333333333r

Simplifying
g = -0.3333333333r
Subproblem 2
Set the factor '(7g + -1r)' equal to zero and attempt to solve:

Simplifying
7g + -1r = 0

Solving
7g + -1r = 0

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

Add 'r' to each side of the equation.
7g + -1r + r = 0 + r

Combine like terms: -1r + r = 0
7g + 0 = 0 + r
7g = 0 + r
Remove the zero:
7g = r

Divide each side by '7'.
g = 0.1428571429r

Simplifying
g = 0.1428571429r
Solution
g = {-0.3333333333r, 0.1428571429r}