x(t)=t(u(t)-u(t-2))

Solution for x(t)=t(u(t)-u(t-2)) equation:

Simplifying
x(t) = t(u(t) + -1u(t + -2))

Multiply x * t
tx = t(u(t) + -1u(t + -2))

Multiply u * t
tx = t(tu + -1u(t + -2))

Reorder the terms:
tx = t(tu + -1u(-2 + t))
tx = t(tu + (-2 * -1u + t * -1u))

Reorder the terms:
tx = t(tu + (-1tu + 2u))
tx = t(tu + (-1tu + 2u))

Combine like terms: tu + -1tu = 0
tx = t(0 + 2u)
tx = t(2u)

Remove parenthesis around (2u)
tx = t * 2u

Reorder the terms for easier multiplication:
tx = 2t * u

Multiply t * u
tx = 2tu

Solving
tx = 2tu

Solving for variable 't'.

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

Add '-2tu' to each side of the equation.
-2tu + tx = 2tu + -2tu

Combine like terms: 2tu + -2tu = 0
-2tu + tx = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-2u + x) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

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

Simplifying
-2u + x = 0

Solving
-2u + x = 0

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

Add '2u' to each side of the equation.
-2u + 2u + x = 0 + 2u

Combine like terms: -2u + 2u = 0
0 + x = 0 + 2u
x = 0 + 2u
Remove the zero:
x = 2u

Add '-1x' to each side of the equation.
x + -1x = 2u + -1x

Combine like terms: x + -1x = 0
0 = 2u + -1x

Simplifying
0 = 2u + -1x

The solution to this equation could not be determined.

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