Solve this

This type of quadratic equation problem is a classic example of how factoring and expanding can be used to find unknown coefficients. To tackle a problem like this, you start by expanding the left-hand side expression (ax+2)(bx+7) to get abx² + (7a + 2b)x + 14. Since the right side is 15x² + cx + 14, you can compare coefficients: ab = 15, 7a + 2b = c, and the constant term 14 is already matched. Additionally, since a + b = 8, you can use substitution to solve for a and b. From a + b = 8, express b = 8 - a, and substitute into ab = 15 to get a(8 - a) = 15, which simplifies to -a² + 8a - 15 = 0. Solving this quadratic equation for a will give you possible values of a, then find b accordingly, and finally calculate c using c = 7a + 2b. As someone who enjoys math puzzles, I find that breaking the problem into smaller steps makes it less intimidating and more enjoyable. It's a great way to sharpen your algebra skills and logical thinking. Remember, practicing such problems regularly will boost your confidence in solving more complex equations in the future!