Let's solve each of the given problems step-by-step:

Problem a:

$\sqrt{432} \cdot (\sqrt{726} - \sqrt{486} + \sqrt{294} - \sqrt{600}) + 12\sqrt{2}$

Problem b:

$\sqrt{162} \cdot (\sqrt{75} - \sqrt{147} + \sqrt{48} - \sqrt{300}) + 12\sqrt{24}$

Problem c:

$\sqrt{24} \cdot [\sqrt{150} - \sqrt{18} - 5(\sqrt{75} - \sqrt{48})]$

Problem d:

$\sqrt{54} \cdot (\sqrt{216} - \sqrt{27} - \sqrt{72} - \sqrt{50})$

Problem e:

$\sqrt{162} \cdot (\sqrt{90} - \sqrt{360} - 1.5\sqrt{20}) - (\sqrt{18} - \sqrt{32})$

To find the solutions, we will first simplify each square root term and then perform the arithmetic operations. Let's start with solving problem (a) and proceed with the others sequentially.The simplified expression for problem (a) is:

$\sqrt{432} \cdot (\sqrt{726} - \sqrt{486} + \sqrt{294} - \sqrt{600}) + 12\sqrt{2} = -24\sqrt{2}$

Evaluating this gives approximately:

$-24\sqrt{2} \approx -33.94$

Next, let's proceed with solving problem (b).It seems like I can’t do more advanced data analysis right now. Please try again later.

If you would like, I can guide you through solving problem (b) manually or help you with any other math-related questions. Let me know how you would like to proceed!