(2t-ay)(t+2ay)=

Solution for (2t-ay)(t+2ay)= equation:

Simplifying
(2t + -1ay)(t + 2ay) = 0

Reorder the terms:
(-1ay + 2t)(t + 2ay) = 0

Reorder the terms:
(-1ay + 2t)(2ay + t) = 0

Multiply (-1ay + 2t) * (2ay + t)
(-1ay * (2ay + t) + 2t * (2ay + t)) = 0
((2ay * -1ay + t * -1ay) + 2t * (2ay + t)) = 0

Reorder the terms:
((-1aty + -2a2y2) + 2t * (2ay + t)) = 0
((-1aty + -2a2y2) + 2t * (2ay + t)) = 0
(-1aty + -2a2y2 + (2ay * 2t + t * 2t)) = 0
(-1aty + -2a2y2 + (4aty + 2t2)) = 0

Reorder the terms:
(-1aty + 4aty + -2a2y2 + 2t2) = 0

Combine like terms: -1aty + 4aty = 3aty
(3aty + -2a2y2 + 2t2) = 0

Solving
3aty + -2a2y2 + 2t2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-2ay + -1t)(ay + -2t) = 0

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

Simplifying
-2ay + -1t = 0

Solving
-2ay + -1t = 0

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

Add 't' to each side of the equation.
-2ay + -1t + t = 0 + t

Combine like terms: -1t + t = 0
-2ay + 0 = 0 + t
-2ay = 0 + t
Remove the zero:
-2ay = t

Divide each side by '-2y'.
a = -0.5ty-1

Simplifying
a = -0.5ty-1
Subproblem 2
Set the factor '(ay + -2t)' equal to zero and attempt to solve:

Simplifying
ay + -2t = 0

Solving
ay + -2t = 0

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

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

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

Divide each side by 'y'.
a = 2ty-1

Simplifying
a = 2ty-1
Solution
a = {-0.5ty-1, 2ty-1}