r^2+3rg-28g^2=0

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Solution for r^2+3rg-28g^2=0 equation: 


Simplifying
r2 + 3rg + -28g2 = 0

Reorder the terms:
3gr + -28g2 + r2 = 0

Solving
3gr + -28g2 + r2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-7g + -1r)(4g + -1r) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4g + -1r)' equal to zero and attempt to solve:

Simplifying
4g + -1r = 0

Solving
4g + -1r = 0

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

Add 'r' to each side of the equation.
4g + -1r + r = 0 + r

Combine like terms: -1r + r = 0
4g + 0 = 0 + r
4g = 0 + r
Remove the zero:
4g = r

Divide each side by '4'.
g = 0.25r

Simplifying
g = 0.25r
Solution
g = {-0.1428571429r, 0.25r}

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