To solve the equations and inequalities presented in your image, let's break them down systematically.

### a) Equation: \( 9x^3 (x - 3) = 0 \)
This can be solved by setting each factor to zero.

1. \( 9x^3 = 0 \)
- Solution: \( x = 0 \)

2. \( x - 3 = 0 \)
- Solution: \( x = 3 \)

**Solutions:** \( x = 0 \) and \( x = 3 \)

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### b) Inequality: \( \frac{x+3}{3} + \frac{30 - 3}{-3x} > 0 \)

To solve the inequality:

1. First, simplify the terms:
- \( \frac{x + 3}{3} > -\frac{30 - 3}{3x} \)
- Rearranging gives:
- \( \frac{x + 3}{3} + \frac{10 - 1}{x} > 0 \)

2. Find a common denominator and combine the fractions.

3. Analyze the resulting expression to find the intervals where the inequality holds.

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### c) Inequality: \( 3x - 8 > 4x - 10 \)

To solve for \( x \):

1. Rearranging gives:
- \( 3x - 4x > -10 + 8 \)
- \( -x > -2 \)
- Multiply by -1 (remember to flip the inequality):
- \( x < 2 \)

**Solution:** \( x < 2 \)

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### d) Inequality: \( \frac{x - 1 - 7x + 75}{-15} < \frac{x - 3}{5} \)

To solve this inequality:

1. Simplify the fraction on the left:
- \( \frac{-6x + 74}{-15} < \frac{x - 3}{5} \)

2. Clear the fractions by multiplying both sides by \( -15 \) (also flipping the inequality):
- \( 6x - 74 > 3x - 9 \)

3. Rearranging gives:
- \( 6x - 3x > 74 - 9 \)
- \( 3x > 65 \)
- \( x > \frac{65}{3} \)

**Solution:** \( x > \frac{65}{3} \)

With all these steps, you should have complete solutions for each section of the problem! If you need further clarification or assistance, feel free to ask!