6r^2+13rw+6w^2=0

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Solution for 6r^2+13rw+6w^2=0 equation: 


Simplifying
6r2 + 13rw + 6w2 = 0

Reorder the terms:
13rw + 6r2 + 6w2 = 0

Solving
13rw + 6r2 + 6w2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3r + 2w)(2r + 3w) = 0


Subproblem 1
Set the factor '(3r + 2w)' equal to zero and attempt to solve:

Simplifying
3r + 2w = 0

Solving
3r + 2w = 0

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

Add '-2w' to each side of the equation.
3r + 2w + -2w = 0 + -2w

Combine like terms: 2w + -2w = 0
3r + 0 = 0 + -2w
3r = 0 + -2w
Remove the zero:
3r = -2w

Divide each side by '3'.
r = -0.6666666667w

Simplifying
r = -0.6666666667w

Subproblem 2
Set the factor '(2r + 3w)' equal to zero and attempt to solve:

Simplifying
2r + 3w = 0

Solving
2r + 3w = 0

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

Add '-3w' to each side of the equation.
2r + 3w + -3w = 0 + -3w

Combine like terms: 3w + -3w = 0
2r + 0 = 0 + -3w
2r = 0 + -3w
Remove the zero:
2r = -3w

Divide each side by '2'.
r = -1.5w

Simplifying
r = -1.5w
Solution
r = {-0.6666666667w, -1.5w}

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