To solve the equation \( \frac{3}{2}x - \frac{8}{3} + \frac{7}{5}x = -\frac{7}{25} \), we need to find the value of \( x \). Let's go through the steps:

1. **Combine like terms involving \( x \)**:
\[
\frac{3}{2}x + \frac{7}{5}x - \frac{8}{3} = -\frac{7}{25}
\]

2. **Find a common denominator for the coefficients of \( x \)**:
The denominators are 2 and 5. The least common multiple (LCM) of 2 and 5 is 10.

Convert the fractions to have a denominator of 10:
\[
\frac{3}{2}x = \frac{3 \times 5}{2 \times 5}x = \frac{15}{10}x
\]
\[
\frac{7}{5}x = \frac{7 \times 2}{5 \times 2}x = \frac{14}{10}x
\]

Now the equation is:
\[
\frac{15}{10}x + \frac{14}{10}x - \frac{8}{3} = -\frac{7}{25}
\]

3. **Combine the \( x \)-terms**:
\[
\left( \frac{15}{10} + \frac{14}{10} \right)x - \frac{8}{3} = -\frac{7}{25}
\]
\[
\frac{29}{10}x - \frac{8}{3} = -\frac{7}{25}
\]

4. **Isolate the \( x \)-term**:
Add \( \frac{8}{3} \) to both sides to isolate the \( x \)-term:
\[
\frac{29}{10}x = -\frac{7}{25} + \frac{8}{3}
\]

5. **Find a common denominator for the right-hand side**:
The denominators are 25 and 3. The LCM of 25 and 3 is 75.

Convert the fractions to have a denominator of 75:
\[
-\frac{7}{25} = -\frac{7 \times 3}{25 \times 3} = -\frac{21}{75}
\]
\[
\frac{8}{3} = \frac{8 \times 25}{3 \times 25} = \frac{200}{75}
\]

Now the equation is:
\[
\frac{29}{10}x = -\frac{21}{75} + \frac{200}{75}
\]
\[
\frac{29}{10}x = \frac{200 - 21}{75}
\]
\[
\frac{29}{10}x = \frac{179}{75}
\]

6. **Solve for \( x \)**:
Multiply both sides by the reciprocal of \( \frac{29}{10} \):
\[
x = \frac{179}{75} \times \frac{10}{29}
\]
\[
x = \frac{179 \times 10}{75 \times 29}
\]
\[
x = \frac{1790}{2175}
\]

Simplify the fraction by finding the greatest common divisor (GCD) of 1790 and 2175. The GCD is 5:
\[
x = \frac{1790 \div 5}{2175 \div 5}
\]
\[
x = \frac{358}{435}
\]

Simplify further by dividing both the numerator and the denominator by their GCD, which is 1 (since 358 and 435 are co-prime):
\[
x = \frac{358}{435}
\]

Therefore, the solution is:
\[
x = \frac{358}{435}
\]