(14-2x)* -144х'

Could you clarify what you want to do with this expression? It’s a bit ambiguous without the task. Here are a few common interpretations and results:

• Simplify

  • -144 x' (14 − 2x) = 288 (x − 7) x'

• View as a time derivative (x = x(t))

  • -144 (14 − 2x) x' = d/dt [36 (14 − 2x)^2]
  • Since d/dt [36 (14 − 2x)^2] = -144 (14 − 2x) x'

• Integrate with respect to t

  • ∫ -144 (14 − 2x) x' dt = 36 (14 − 2x)^2 + C
  • (Equivalently, treating dx = x' dt, ∫ -144 (14 − 2x) dx = -144 (14x − x^2) + C, which differs by a constant from the previous form.)

• Solve a differential equation if you mean -144 (14 − 2x) x' = 0

  • Solutions: x'(t) = 0 or 14 − 2x = 0
  • This gives x(t) = constant (any constant), and in particular x ≡ 7 is included.

If you can tell me which of these matches your problem (or provide the exact task statement), I’ll give a full, step-by-step solution aligned to that.