6q^2-13qt-63t^2=0

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Solution for 6q^2-13qt-63t^2=0 equation: 


Simplifying
6q2 + -13qt + -63t2 = 0

Reorder the terms:
-13qt + 6q2 + -63t2 = 0

Solving
-13qt + 6q2 + -63t2 = 0

Solving for variable 'q'.

Factor a trinomial.
(2q + -9t)(3q + 7t) = 0


Subproblem 1
Set the factor '(2q + -9t)' equal to zero and attempt to solve:

Simplifying
2q + -9t = 0

Solving
2q + -9t = 0

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

Add '9t' to each side of the equation.
2q + -9t + 9t = 0 + 9t

Combine like terms: -9t + 9t = 0
2q + 0 = 0 + 9t
2q = 0 + 9t
Remove the zero:
2q = 9t

Divide each side by '2'.
q = 4.5t

Simplifying
q = 4.5t

Subproblem 2
Set the factor '(3q + 7t)' equal to zero and attempt to solve:

Simplifying
3q + 7t = 0

Solving
3q + 7t = 0

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

Add '-7t' to each side of the equation.
3q + 7t + -7t = 0 + -7t

Combine like terms: 7t + -7t = 0
3q + 0 = 0 + -7t
3q = 0 + -7t
Remove the zero:
3q = -7t

Divide each side by '3'.
q = -2.333333333t

Simplifying
q = -2.333333333t
Solution
q = {4.5t, -2.333333333t}

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