1. The problem states: Forty-five less a number is equal to the product of 3 and the sum of the number and 7. 2. Let the number be $x$. 3. "Forty-five less a number" translates to $x - 45$. 4. "The product of 3 and the sum of the number and 7" translates to $3(x + 7)$. 5. The equation is therefore: $$x - 45 = 3(x + 7)$$ 6. This is the equation as requested, without simplification.