X(t)=1-u(t-3)+(t*u(t-3))

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Solution for X(t)=1-u(t-3)+(t*u(t-3)) equation: 


Simplifying
X(t) = 1 + -1u(t + -3) + (t * u(t + -3))

Multiply X * t
tX = 1 + -1u(t + -3) + (t * u(t + -3))

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

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

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

Multiply t * u
tX = 1 + -1tu + 3u + (tu(-3 + t))
tX = 1 + -1tu + 3u + ((-3 * tu + t * tu))
tX = 1 + -1tu + 3u + ((-3tu + t2u))
tX = 1 + -1tu + 3u + (-3tu + t2u)

Remove parenthesis around (-3tu + t2u)
tX = 1 + -1tu + 3u + -3tu + t2u

Reorder the terms:
tX = 1 + -1tu + -3tu + t2u + 3u

Combine like terms: -1tu + -3tu = -4tu
tX = 1 + -4tu + t2u + 3u

Solving
tX = 1 + -4tu + t2u + 3u

Solving for variable 't'.

Reorder the terms:
-1 + tX + 4tu + -1t2u + -3u = 1 + -4tu + t2u + 3u + -1 + 4tu + -1t2u + -3u

Reorder the terms:
-1 + tX + 4tu + -1t2u + -3u = 1 + -1 + -4tu + 4tu + t2u + -1t2u + 3u + -3u

Combine like terms: 1 + -1 = 0
-1 + tX + 4tu + -1t2u + -3u = 0 + -4tu + 4tu + t2u + -1t2u + 3u + -3u
-1 + tX + 4tu + -1t2u + -3u = -4tu + 4tu + t2u + -1t2u + 3u + -3u

Combine like terms: -4tu + 4tu = 0
-1 + tX + 4tu + -1t2u + -3u = 0 + t2u + -1t2u + 3u + -3u
-1 + tX + 4tu + -1t2u + -3u = t2u + -1t2u + 3u + -3u

Combine like terms: t2u + -1t2u = 0
-1 + tX + 4tu + -1t2u + -3u = 0 + 3u + -3u
-1 + tX + 4tu + -1t2u + -3u = 3u + -3u

Combine like terms: 3u + -3u = 0
-1 + tX + 4tu + -1t2u + -3u = 0

The solution to this equation could not be determined.

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