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To solve for \( y \) in the equation
\[
b^4c - 7 = \frac{by}{c} \cdot 7,
\]
we can first simplify the right side of the equation:
\[
b^4c - 7 = \frac{7by}{c}.
\]
Next, we can multiply both sides by \( c \) to eliminate the fraction:
\[
c(b^4c - 7) = 7by.
\]
This simplifies to:
\[
cb^4c - 7c = 7by.
\]
Now, we want to isolate \( y \). We can divide both sides by \( 7b \) (assuming \( b \neq 0 \)):
\[
y = \frac{cb^4c - 7c}{7b}.
\]
This can be simplified further:
\[
y = \frac{c(b^4c - 7)}{7b}.
\]
So, the final expression for \( y \) is:
\[
y = \frac{c(b^4c - 7)}{7b}.
\]