$$-38 = 3(4d+7)+5(7d+7)$$

$$ \begin{aligned} -38 &= 3(4d+7)+5(7d+7)&& \text{simplify right side} \\[1 em]-38 &= 12d+21+35d+35&& \\[1 em]-38 &= 47d+56&& \text{ swap the left and right side of the equation } \\[1 em]47d+56 &= -38&& \text{ move 56 to the right } \\[1 em]47d &= -38-56&& \\[1 em]47d &= -94&& \text{ divide both sides by $ 47 $ } \\[1 em]d &= -\frac{94}{47}&& \\[1 em]d &= -2&& \\[1 em] \end{aligned} $$

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