B= -3-2/3+3/5(-10/9-25/3)-5/6

Let's simplify the expression step by step.

The equation is:

\[
B = -3 - \frac{2}{3} + \frac{3}{5} \left( -\frac{10}{9} - \frac{25}{3} \right) - \frac{5}{6}
\]

1. First, let's simplify the term inside the parentheses:

\[
-\frac{10}{9} - \frac{25}{3}
\]

To combine these, we need a common denominator. The least common multiple of \(9\) and \(3\) is \(9\).

Rewrite \(-\frac{25}{3}\) with a denominator of \(9\):

\[
-\frac{25}{3} = -\frac{25 \times 3}{3 \times 3} = -\frac{75}{9}
\]

Now combine:

\[
-\frac{10}{9} - \frac{75}{9} = -\frac{10 + 75}{9} = -\frac{85}{9}
\]

2. Now substitute this back into the original equation:

\[
B = -3 - \frac{2}{3} + \frac{3}{5} \left( -\frac{85}{9} \right) - \frac{5}{6}
\]

3. Next, calculate \(\frac{3}{5} \left(-\frac{85}{9}\right)\):

\[
\frac{3}{5} \cdot -\frac{85}{9} = -\frac{3 \cdot 85}{5 \cdot 9} = -\frac{255}{45}
\]

We can simplify \(-\frac{255}{45}\):

Both numerator and denominator are divisible by \(15\):

\[
-\frac{255 \div 15}{45 \div 15} = -\frac{17}{3}
\]

4. Now substitute this back into the equation:

\[
B = -3 - \frac{2}{3} - \frac{17}{3} - \frac{5}{6}
\]

5. Next, combine the fractions. First, convert \(-3\) to a fraction:

\[
-3 = -\frac{9}{3}
\]

Now we can add:

\[
B = -\frac{9}{3} - \frac{2}{3} - \frac{17}{3} - \frac{5}{6}
\]

Combine the first three terms:

\[
B = -\frac{9 + 2 + 17}{3} - \frac{5}{6} = -\frac{28}{3} - \frac{5}{6}
\]

6. Now we need a common denominator to add \(-\frac{28}{3}\) and \(-\frac{5}{6}\). The least common multiple of \(3\) and \(6\) is \(6\):

Convert \(-\frac{28}{3}\):

\[
-\frac{28}{3} = -\frac{28 \times 2}{3 \times 2} = -\frac{56}{6}
\]

7. Now combine:

\[
B = -\frac{56}{6} - \frac{5}{6} = -\frac{56 + 5}{6} = -\frac{61}{6}
\]

So, the final value of \(B\) is:

\[
B = -\frac{61}{6}
\]