How do I factor each of these?

ab+cd=38ac+bd=34ad+bc=43 \begin{aligned} ab+cd&=&38 \\ ac+bd&=&34\\ ad+bc&=&43\\ \end{aligned}

Let a,b,ca,b,c and dd positive integers such that they satisfy the system of equations above. Find a+b+c+da+b+c+d.

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