r^2-2rg-80g^2=

Solution for r^2-2rg-80g^2= equation:

Simplifying
r2 + -2rg + -80g2 = 0

Reorder the terms:
-2gr + -80g2 + r2 = 0

Solving
-2gr + -80g2 + r2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-8g + -1r)(10g + -1r) = 0

Subproblem 1
Set the factor '(-8g + -1r)' equal to zero and attempt to solve:

Simplifying
-8g + -1r = 0

Solving
-8g + -1r = 0

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

Add 'r' to each side of the equation.
-8g + -1r + r = 0 + r

Combine like terms: -1r + r = 0
-8g + 0 = 0 + r
-8g = 0 + r
Remove the zero:
-8g = r

Divide each side by '-8'.
g = -0.125r

Simplifying
g = -0.125r
Subproblem 2
Set the factor '(10g + -1r)' equal to zero and attempt to solve:

Simplifying
10g + -1r = 0

Solving
10g + -1r = 0

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

Add 'r' to each side of the equation.
10g + -1r + r = 0 + r

Combine like terms: -1r + r = 0
10g + 0 = 0 + r
10g = 0 + r
Remove the zero:
10g = r

Divide each side by '10'.
g = 0.1r

Simplifying
g = 0.1r
Solution
g = {-0.125r, 0.1r}