x(t)=u(t-3)-u(t+3)

Solution for x(t)=u(t-3)-u(t+3) equation:

Simplifying
x(t) = u(t + -3) + -1u(t + 3)

Multiply x * t
tx = u(t + -3) + -1u(t + 3)

Reorder the terms:
tx = u(-3 + t) + -1u(t + 3)
tx = (-3 * u + t * u) + -1u(t + 3)

Reorder the terms:
tx = (tu + -3u) + -1u(t + 3)
tx = (tu + -3u) + -1u(t + 3)

Reorder the terms:
tx = tu + -3u + -1u(3 + t)
tx = tu + -3u + (3 * -1u + t * -1u)

Reorder the terms:
tx = tu + -3u + (-1tu + -3u)
tx = tu + -3u + (-1tu + -3u)

Reorder the terms:
tx = tu + -1tu + -3u + -3u

Combine like terms: tu + -1tu = 0
tx = 0 + -3u + -3u
tx = -3u + -3u

Combine like terms: -3u + -3u = -6u
tx = -6u

Solving
tx = -6u

Solving for variable 't'.

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

Divide each side by 'x'.
t = -6ux-1

Simplifying
t = -6ux-1