Solve for B
\left\{\begin{matrix}\\B=\frac{2C}{3}\text{, }&\text{unconditionally}\\B\in \mathrm{R}\text{, }&E=0\end{matrix}\right.
Solve for C
\left\{\begin{matrix}\\C=\frac{3B}{2}\text{, }&\text{unconditionally}\\C\in \mathrm{R}\text{, }&E=0\end{matrix}\right.
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3BE-2EC=0
Anything times zero gives zero.
3BE=2EC
Add 2EC to both sides. Anything plus zero gives itself.
3EB=2CE
The equation is in standard form.
\frac{3EB}{3E}=\frac{2CE}{3E}
Divide both sides by 3E.
B=\frac{2CE}{3E}
Dividing by 3E undoes the multiplication by 3E.
B=\frac{2C}{3}
Divide 2EC by 3E.
3BE-2EC=0
Anything times zero gives zero.
-2EC=-3BE
Subtract 3BE from both sides. Anything subtracted from zero gives its negation.
\left(-2E\right)C=-3BE
The equation is in standard form.
\frac{\left(-2E\right)C}{-2E}=-\frac{3BE}{-2E}
Divide both sides by -2E.
C=-\frac{3BE}{-2E}
Dividing by -2E undoes the multiplication by -2E.
C=\frac{3B}{2}
Divide -3BE by -2E.
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