18a^2-27at+10t^2=

Solution for 18a^2-27at+10t^2= equation:

Simplifying
18a2 + -27at + 10t2 = 0

Reorder the terms:
-27at + 18a2 + 10t2 = 0

Solving
-27at + 18a2 + 10t2 = 0

Solving for variable 'a'.

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

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

Simplifying
6a + -5t = 0

Solving
6a + -5t = 0

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

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

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

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

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

Simplifying
3a + -2t = 0

Solving
3a + -2t = 0

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

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

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

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

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