To solve this equation, we need to isolate the variable x on one side of the equation.

First, let's start by moving all the terms involving x to one side of the equation.

-1.5x + 4 = -0.9x - 5

Add 0.9x to both sides:

-1.5x + 0.9x + 4 = -5

Now, combine like terms:

-0.6x + 4 = -5

Next, subtract 4 from both sides:

-0.6x = -9

Finally, divide by -0.6 to solve for x:

x = -9 / -0.6

x = 15

Therefore, the solution to the equation -1.5x + 4 = -0.9x - 5 is x = 15.