90q^2-57qt-189t^2=0

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Solution for 90q^2-57qt-189t^2=0 equation: 


Simplifying
90q2 + -57qt + -189t2 = 0

Reorder the terms:
-57qt + 90q2 + -189t2 = 0

Solving
-57qt + 90q2 + -189t2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-19qt + 30q2 + -63t2) = 0

Factor a trinomial.
3((5q + -9t)(6q + 7t)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5q + -9t)' equal to zero and attempt to solve:

Simplifying
5q + -9t = 0

Solving
5q + -9t = 0

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

Add '9t' to each side of the equation.
5q + -9t + 9t = 0 + 9t

Combine like terms: -9t + 9t = 0
5q + 0 = 0 + 9t
5q = 0 + 9t
Remove the zero:
5q = 9t

Divide each side by '5'.
q = 1.8t

Simplifying
q = 1.8t

Subproblem 2
Set the factor '(6q + 7t)' equal to zero and attempt to solve:

Simplifying
6q + 7t = 0

Solving
6q + 7t = 0

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

Add '-7t' to each side of the equation.
6q + 7t + -7t = 0 + -7t

Combine like terms: 7t + -7t = 0
6q + 0 = 0 + -7t
6q = 0 + -7t
Remove the zero:
6q = -7t

Divide each side by '6'.
q = -1.166666667t

Simplifying
q = -1.166666667t
Solution
q = {1.8t, -1.166666667t}

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