Regroup terms.
\[21lmnn{n}^{2}fty\imath \imath -2n\times 2{n}^{2}+3m=1\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[21lm{n}^{1+1+2}fty\imath \imath -2n\times 2{n}^{2}+3m=1\]
Simplify \(1+1\) to \(2\).
\[21lm{n}^{2+2}fty\imath \imath -2n\times 2{n}^{2}+3m=1\]
Simplify \(2+2\) to \(4\).
\[21lm{n}^{4}fty\imath \imath -2n\times 2{n}^{2}+3m=1\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[21lm{n}^{4}fty{\imath }^{2}-2n\times 2{n}^{2}+3m=1\]
Use Square Rule: \({i}^{2}=-1\).
\[21lm{n}^{4}fty\times -1-2n\times 2{n}^{2}+3m=1\]
Simplify \(21lm{n}^{4}fty\times -1\) to \(-21lm{n}^{4}fty\).
\[-21lm{n}^{4}fty-2n\times 2{n}^{2}+3m=1\]
Take out the constants.
\[-21lm{n}^{4}fty-(2\times 2)n{n}^{2}+3m=1\]
Simplify \(2\times 2\) to \(4\).
\[-21lm{n}^{4}fty-4n{n}^{2}+3m=1\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[-21lm{n}^{4}fty-4{n}^{1+2}+3m=1\]
Simplify \(1+2\) to \(3\).
\[-21lm{n}^{4}fty-4{n}^{3}+3m=1\]
Add \(4{n}^{3}\) to both sides.
\[-21lm{n}^{4}fty+3m=1+4{n}^{3}\]
Factor out the common term \(3m\).
\[-3m(7l{n}^{4}fty-1)=1+4{n}^{3}\]
Divide both sides by \(-3\).
\[m(7l{n}^{4}fty-1)=-\frac{1+4{n}^{3}}{3}\]
Divide both sides by \(m\).
\[7l{n}^{4}fty-1=-\frac{\frac{1+4{n}^{3}}{3}}{m}\]
Simplify \(\frac{\frac{1+4{n}^{3}}{3}}{m}\) to \(\frac{1+4{n}^{3}}{3m}\).
\[7l{n}^{4}fty-1=-\frac{1+4{n}^{3}}{3m}\]
Add \(1\) to both sides.
\[7l{n}^{4}fty=-\frac{1+4{n}^{3}}{3m}+1\]
Divide both sides by \(7\).
\[l{n}^{4}fty=\frac{-\frac{1+4{n}^{3}}{3m}+1}{7}\]
Simplify \(\frac{-\frac{1+4{n}^{3}}{3m}+1}{7}\) to \(-\frac{\frac{1+4{n}^{3}}{3m}}{7}+\frac{1}{7}\).
\[l{n}^{4}fty=-\frac{\frac{1+4{n}^{3}}{3m}}{7}+\frac{1}{7}\]
Simplify \(\frac{\frac{1+4{n}^{3}}{3m}}{7}\) to \(\frac{1+4{n}^{3}}{3\times 7m}\).
\[l{n}^{4}fty=-\frac{1+4{n}^{3}}{3\times 7m}+\frac{1}{7}\]
Simplify \(3\times 7m\) to \(21m\).
\[l{n}^{4}fty=-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}\]
Divide both sides by \({n}^{4}\).
\[lfty=\frac{-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}}{{n}^{4}}\]
Divide both sides by \(f\).
\[lty=\frac{\frac{-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}}{{n}^{4}}}{f}\]
Simplify \(\frac{\frac{-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}}{{n}^{4}}}{f}\) to \(\frac{-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}}{{n}^{4}f}\).
\[lty=\frac{-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}}{{n}^{4}f}\]
Divide both sides by \(t\).
\[ly=\frac{\frac{-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}}{{n}^{4}f}}{t}\]
Simplify \(\frac{\frac{-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}}{{n}^{4}f}}{t}\) to \(\frac{-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}}{{n}^{4}ft}\).
\[ly=\frac{-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}}{{n}^{4}ft}\]
Divide both sides by \(y\).
\[l=\frac{\frac{-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}}{{n}^{4}ft}}{y}\]
Simplify \(\frac{\frac{-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}}{{n}^{4}ft}}{y}\) to \(\frac{-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}}{{n}^{4}fty}\).
\[l=\frac{-\frac{1+4{n}^{3}}{21m}+\frac{1}{7}}{{n}^{4}fty}\]
l=(-(1+4*n^3)/(21*m)+1/7)/(n^4*f*t*y)
