r^2+10rg+16g^2=

Solution for r^2+10rg+16g^2= equation:

Simplifying
r2 + 10rg + 16g2 = 0

Reorder the terms:
10gr + 16g2 + r2 = 0

Solving
10gr + 16g2 + r2 = 0

Solving for variable 'g'.

Factor a trinomial.
(8g + r)(2g + r) = 0

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

Simplifying
8g + r = 0

Solving
8g + r = 0

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

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

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

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

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

Simplifying
2g + r = 0

Solving
2g + r = 0

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

Add '-1r' to each side of the equation.
2g + r + -1r = 0 + -1r

Combine like terms: r + -1r = 0
2g + 0 = 0 + -1r
2g = 0 + -1r
Remove the zero:
2g = -1r

Divide each side by '2'.
g = -0.5r

Simplifying
g = -0.5r
Solution
g = {-0.125r, -0.5r}