A(t-3)(t-5)=0

Solution for A(t-3)(t-5)=0 equation:

Simplifying
A(t + -3)(t + -5) = 0

Reorder the terms:
A(-3 + t)(t + -5) = 0

Reorder the terms:
A(-3 + t)(-5 + t) = 0

Multiply (-3 + t) * (-5 + t)
A(-3(-5 + t) + t(-5 + t)) = 0
A((-5 * -3 + t * -3) + t(-5 + t)) = 0
A((15 + -3t) + t(-5 + t)) = 0
A(15 + -3t + (-5 * t + t * t)) = 0
A(15 + -3t + (-5t + t2)) = 0

Combine like terms: -3t + -5t = -8t
A(15 + -8t + t2) = 0
(15 * A + -8t * A + t2 * A) = 0
(15A + -8tA + t2A) = 0

Solving
15A + -8tA + t2A = 0

Solving for variable 'A'.

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

Factor out the Greatest Common Factor (GCF), 'A'.
A(15 + -8t + t2) = 0

Factor a trinomial.
A((3 + -1t)(5 + -1t)) = 0

Subproblem 1
Set the factor 'A' equal to zero and attempt to solve:

Simplifying
A = 0

Solving
A = 0

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

Simplifying
A = 0
Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Add 't' to each side of the equation.
-1t + t = -3 + t

Combine like terms: -1t + t = 0
0 = -3 + t

Simplifying
0 = -3 + t

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Add 't' to each side of the equation.
-1t + t = -5 + t

Combine like terms: -1t + t = 0
0 = -5 + t

Simplifying
0 = -5 + t

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
A = {0}