18q^2-27qt+10t^2=0

Solution for 18q^2-27qt+10t^2=0 equation:

Simplifying
18q2 + -27qt + 10t2 = 0

Reorder the terms:
-27qt + 18q2 + 10t2 = 0

Solving
-27qt + 18q2 + 10t2 = 0

Solving for variable 'q'.

Factor a trinomial.
(6q + -5t)(3q + -2t) = 0

Subproblem 1
Set the factor '(6q + -5t)' equal to zero and attempt to solve:

Simplifying
6q + -5t = 0

Solving
6q + -5t = 0

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

Add '5t' to each side of the equation.
6q + -5t + 5t = 0 + 5t

Combine like terms: -5t + 5t = 0
6q + 0 = 0 + 5t
6q = 0 + 5t
Remove the zero:
6q = 5t

Divide each side by '6'.
q = 0.8333333333t

Simplifying
q = 0.8333333333t
Subproblem 2
Set the factor '(3q + -2t)' equal to zero and attempt to solve:

Simplifying
3q + -2t = 0

Solving
3q + -2t = 0

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

Add '2t' to each side of the equation.
3q + -2t + 2t = 0 + 2t

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

Divide each side by '3'.
q = 0.6666666667t

Simplifying
q = 0.6666666667t
Solution
q = {0.8333333333t, 0.6666666667t}