Solve for S (complex solution)
\left\{\begin{matrix}S=\frac{x+b}{15b}\text{, }&b\neq 0\\S\in \mathrm{C}\text{, }&b=0\text{ and }x=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=\frac{x}{15S-1}\text{, }&S\neq \frac{1}{15}\\b\in \mathrm{C}\text{, }&x=0\text{ and }S=\frac{1}{15}\end{matrix}\right.
Solve for S
\left\{\begin{matrix}S=\frac{x+b}{15b}\text{, }&b\neq 0\\S\in \mathrm{R}\text{, }&b=0\text{ and }x=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=\frac{x}{15S-1}\text{, }&S\neq \frac{1}{15}\\b\in \mathrm{R}\text{, }&x=0\text{ and }S=\frac{1}{15}\end{matrix}\right.
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b\times 5S=\frac{1}{3}x+\frac{1}{3}b
Use the distributive property to multiply \frac{1}{3} by x+b.
5bS=\frac{x+b}{3}
The equation is in standard form.
\frac{5bS}{5b}=\frac{x+b}{3\times 5b}
Divide both sides by 5b.
S=\frac{x+b}{3\times 5b}
Dividing by 5b undoes the multiplication by 5b.
S=\frac{x+b}{15b}
Divide \frac{x+b}{3} by 5b.
b\times 5S=\frac{1}{3}x+\frac{1}{3}b
Use the distributive property to multiply \frac{1}{3} by x+b.
b\times 5S-\frac{1}{3}b=\frac{1}{3}x
Subtract \frac{1}{3}b from both sides.
\left(5S-\frac{1}{3}\right)b=\frac{1}{3}x
Combine all terms containing b.
\left(5S-\frac{1}{3}\right)b=\frac{x}{3}
The equation is in standard form.
\frac{\left(5S-\frac{1}{3}\right)b}{5S-\frac{1}{3}}=\frac{x}{3\left(5S-\frac{1}{3}\right)}
Divide both sides by 5S-\frac{1}{3}.
b=\frac{x}{3\left(5S-\frac{1}{3}\right)}
Dividing by 5S-\frac{1}{3} undoes the multiplication by 5S-\frac{1}{3}.
b=\frac{x}{15S-1}
Divide \frac{x}{3} by 5S-\frac{1}{3}.
b\times 5S=\frac{1}{3}x+\frac{1}{3}b
Use the distributive property to multiply \frac{1}{3} by x+b.
5bS=\frac{x+b}{3}
The equation is in standard form.
\frac{5bS}{5b}=\frac{x+b}{3\times 5b}
Divide both sides by 5b.
S=\frac{x+b}{3\times 5b}
Dividing by 5b undoes the multiplication by 5b.
S=\frac{x+b}{15b}
Divide \frac{x+b}{3} by 5b.
b\times 5S=\frac{1}{3}x+\frac{1}{3}b
Use the distributive property to multiply \frac{1}{3} by x+b.
b\times 5S-\frac{1}{3}b=\frac{1}{3}x
Subtract \frac{1}{3}b from both sides.
\left(5S-\frac{1}{3}\right)b=\frac{1}{3}x
Combine all terms containing b.
\left(5S-\frac{1}{3}\right)b=\frac{x}{3}
The equation is in standard form.
\frac{\left(5S-\frac{1}{3}\right)b}{5S-\frac{1}{3}}=\frac{x}{3\left(5S-\frac{1}{3}\right)}
Divide both sides by 5S-\frac{1}{3}.
b=\frac{x}{3\left(5S-\frac{1}{3}\right)}
Dividing by 5S-\frac{1}{3} undoes the multiplication by 5S-\frac{1}{3}.
b=\frac{x}{15S-1}
Divide \frac{x}{3} by 5S-\frac{1}{3}.
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