(t+x+3)dt+dx=0

Solution for (t+x+3)dt+dx=0 equation:

Simplifying
(t + x + 3) * dt + dx = 0

Reorder the terms:
(3 + t + x) * dt + dx = 0

Reorder the terms for easier multiplication:
dt(3 + t + x) + dx = 0
(3 * dt + t * dt + x * dt) + dx = 0

Reorder the terms:
(3dt + dtx + dt2) + dx = 0
(3dt + dtx + dt2) + dx = 0

Solving
3dt + dtx + dt2 + dx = 0

Solving for variable 'd'.

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

Factor out the Greatest Common Factor (GCF), 'd'.
d(3t + tx + t2 + x) = 0

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

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0
Subproblem 2
Set the factor '(3t + tx + t2 + x)' equal to zero and attempt to solve:

Simplifying
3t + tx + t2 + x = 0

Solving
3t + tx + t2 + x = 0

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

Add '-3t' to each side of the equation.
3t + tx + t2 + -3t + x = 0 + -3t

Reorder the terms:
3t + -3t + tx + t2 + x = 0 + -3t

Combine like terms: 3t + -3t = 0
0 + tx + t2 + x = 0 + -3t
tx + t2 + x = 0 + -3t
Remove the zero:
tx + t2 + x = -3t

Add '-1tx' to each side of the equation.
tx + t2 + -1tx + x = -3t + -1tx

Reorder the terms:
tx + -1tx + t2 + x = -3t + -1tx

Combine like terms: tx + -1tx = 0
0 + t2 + x = -3t + -1tx
t2 + x = -3t + -1tx

Add '-1t2' to each side of the equation.
t2 + -1t2 + x = -3t + -1tx + -1t2

Combine like terms: t2 + -1t2 = 0
0 + x = -3t + -1tx + -1t2
x = -3t + -1tx + -1t2

Add '-1x' to each side of the equation.
x + -1x = -3t + -1tx + -1t2 + -1x

Combine like terms: x + -1x = 0
0 = -3t + -1tx + -1t2 + -1x

Simplifying
0 = -3t + -1tx + -1t2 + -1x

The solution to this equation could not be determined.

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