1. **State the problem:** Simplify the expression $ (5x + 3)(x - 1)(3x - 2) $. 2. **Multiply the first two binomials:** $$ (5x + 3)(x - 1) = 5x \cdot x + 5x \cdot (-1) + 3 \cdot x + 3 \cdot (-1) = 5x^2 - 5x + 3x - 3 = 5x^2 - 2x - 3 $$ 3. **Multiply the result by the third binomial:** $$ (5x^2 - 2x - 3)(3x - 2) $$ Expand term-by-term: $$ 5x^2 \cdot 3x = 15x^3 $$ $$ 5x^2 \cdot (-2) = -10x^2 $$ $$ (-2x) \cdot 3x = -6x^2 $$ $$ (-2x) \cdot (-2) = 4x $$ $$ (-3) \cdot 3x = -9x $$ $$ (-3) \cdot (-2) = 6 $$ 4. **Combine like terms:** $$ 15x^3 + (-10x^2 - 6x^2) + (4x - 9x) + 6 = 15x^3 - 16x^2 - 5x + 6 $$ **Final answer:** $$ \boxed{15x^3 - 16x^2 - 5x + 6} $$