Solve for N
\left\{\begin{matrix}N=-\frac{F}{10\left(4j-3i\right)}\text{, }&j\neq \frac{3}{4}i\\N\in \mathrm{C}\text{, }&F=0\text{ and }j=\frac{3}{4}i\end{matrix}\right.
Solve for F
F=10N\left(3i-4j\right)
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F=30iN-40jN
Use the distributive property to multiply 30i-40j by N.
30iN-40jN=F
Swap sides so that all variable terms are on the left hand side.
\left(30i-40j\right)N=F
Combine all terms containing N.
\frac{\left(30i-40j\right)N}{30i-40j}=\frac{F}{30i-40j}
Divide both sides by 30i-40j.
N=\frac{F}{30i-40j}
Dividing by 30i-40j undoes the multiplication by 30i-40j.
N=\frac{F}{10\left(3i-4j\right)}
Divide F by 30i-40j.
F=30iN-40jN
Use the distributive property to multiply 30i-40j by N.
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