Take out the constants.
\[PIN-(152\times 3\times 4\times 6\times 5)a{a}^{2}{b}^{2}{b}^{3}c=2X\times 3\]
Simplify \(152\times 3\) to \(456\).
\[PIN-(456\times 4\times 6\times 5)a{a}^{2}{b}^{2}{b}^{3}c=2X\times 3\]
Simplify \(456\times 4\) to \(1824\).
\[PIN-(1824\times 6\times 5)a{a}^{2}{b}^{2}{b}^{3}c=2X\times 3\]
Simplify \(1824\times 6\) to \(10944\).
\[PIN-(10944\times 5)a{a}^{2}{b}^{2}{b}^{3}c=2X\times 3\]
Simplify \(10944\times 5\) to \(54720\).
\[PIN-54720a{a}^{2}{b}^{2}{b}^{3}c=2X\times 3\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[PIN-54720{a}^{1+2}{b}^{2+3}c=2X\times 3\]
Simplify \(1+2\) to \(3\).
\[PIN-54720{a}^{3}{b}^{2+3}c=2X\times 3\]
Simplify \(2+3\) to \(5\).
\[PIN-54720{a}^{3}{b}^{5}c=2X\times 3\]
Simplify \(2X\times 3\) to \(6X\).
\[PIN-54720{a}^{3}{b}^{5}c=6X\]
Subtract \(PIN\) from both sides.
\[-54720{a}^{3}{b}^{5}c=6X-PIN\]
Divide both sides by \(-54720\).
\[{a}^{3}{b}^{5}c=-\frac{6X-PIN}{54720}\]
Divide both sides by \({a}^{3}\).
\[{b}^{5}c=-\frac{\frac{6X-PIN}{54720}}{{a}^{3}}\]
Simplify \(\frac{\frac{6X-PIN}{54720}}{{a}^{3}}\) to \(\frac{6X-PIN}{54720{a}^{3}}\).
\[{b}^{5}c=-\frac{6X-PIN}{54720{a}^{3}}\]
Divide both sides by \({b}^{5}\).
\[c=-\frac{\frac{6X-PIN}{54720{a}^{3}}}{{b}^{5}}\]
Simplify \(\frac{\frac{6X-PIN}{54720{a}^{3}}}{{b}^{5}}\) to \(\frac{6X-PIN}{54720{a}^{3}{b}^{5}}\).
\[c=-\frac{6X-PIN}{54720{a}^{3}{b}^{5}}\]
c=-(6*X-PIN)/(54720*a^3*b^5)
