r^2+14rg+49g^2=

Solution for r^2+14rg+49g^2= equation:

Simplifying
r2 + 14rg + 49g2 = 0

Reorder the terms:
14gr + 49g2 + r2 = 0

Solving
14gr + 49g2 + r2 = 0

Solving for variable 'g'.

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

Subproblem 1
Set the factor '(7g + r)' equal to zero and attempt to solve:

Simplifying
7g + r = 0

Solving
7g + r = 0

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

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

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

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

Simplifying
g = -0.1428571429r
Subproblem 2
Set the factor '(7g + r)' equal to zero and attempt to solve:

Simplifying
7g + r = 0

Solving
7g + r = 0

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

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

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

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

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