6q^2-7qr-24r^2=0

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Solution for 6q^2-7qr-24r^2=0 equation: 


Simplifying
6q2 + -7qr + -24r2 = 0

Reorder the terms:
-7qr + 6q2 + -24r2 = 0

Solving
-7qr + 6q2 + -24r2 = 0

Solving for variable 'q'.

Factor a trinomial.
(3q + -8r)(2q + 3r) = 0


Subproblem 1
Set the factor '(3q + -8r)' equal to zero and attempt to solve:

Simplifying
3q + -8r = 0

Solving
3q + -8r = 0

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

Add '8r' to each side of the equation.
3q + -8r + 8r = 0 + 8r

Combine like terms: -8r + 8r = 0
3q + 0 = 0 + 8r
3q = 0 + 8r
Remove the zero:
3q = 8r

Divide each side by '3'.
q = 2.666666667r

Simplifying
q = 2.666666667r

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

Simplifying
2q + 3r = 0

Solving
2q + 3r = 0

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

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

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

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

Simplifying
q = -1.5r
Solution
q = {2.666666667r, -1.5r}

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