Solve for c (complex solution)
\left\{\begin{matrix}c=-\frac{x-18}{15f}\text{, }&f\neq 0\\c\in \mathrm{C}\text{, }&x=18\text{ and }f=0\end{matrix}\right.
Solve for f (complex solution)
\left\{\begin{matrix}f=-\frac{x-18}{15c}\text{, }&c\neq 0\\f\in \mathrm{C}\text{, }&x=18\text{ and }c=0\end{matrix}\right.
Solve for c
\left\{\begin{matrix}c=-\frac{x-18}{15f}\text{, }&f\neq 0\\c\in \mathrm{R}\text{, }&x=18\text{ and }f=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=-\frac{x-18}{15c}\text{, }&c\neq 0\\f\in \mathrm{R}\text{, }&x=18\text{ and }c=0\end{matrix}\right.
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18-3x+2x=15fc
Use the distributive property to multiply 3 by 6-x.
18-x=15fc
Combine -3x and 2x to get -x.
15fc=18-x
Swap sides so that all variable terms are on the left hand side.
\frac{15fc}{15f}=\frac{18-x}{15f}
Divide both sides by 15f.
c=\frac{18-x}{15f}
Dividing by 15f undoes the multiplication by 15f.
18-3x+2x=15fc
Use the distributive property to multiply 3 by 6-x.
18-x=15fc
Combine -3x and 2x to get -x.
15fc=18-x
Swap sides so that all variable terms are on the left hand side.
15cf=18-x
The equation is in standard form.
\frac{15cf}{15c}=\frac{18-x}{15c}
Divide both sides by 15c.
f=\frac{18-x}{15c}
Dividing by 15c undoes the multiplication by 15c.
18-3x+2x=15fc
Use the distributive property to multiply 3 by 6-x.
18-x=15fc
Combine -3x and 2x to get -x.
15fc=18-x
Swap sides so that all variable terms are on the left hand side.
\frac{15fc}{15f}=\frac{18-x}{15f}
Divide both sides by 15f.
c=\frac{18-x}{15f}
Dividing by 15f undoes the multiplication by 15f.
18-3x+2x=15fc
Use the distributive property to multiply 3 by 6-x.
18-x=15fc
Combine -3x and 2x to get -x.
15fc=18-x
Swap sides so that all variable terms are on the left hand side.
15cf=18-x
The equation is in standard form.
\frac{15cf}{15c}=\frac{18-x}{15c}
Divide both sides by 15c.
f=\frac{18-x}{15c}
Dividing by 15c undoes the multiplication by 15c.
Examples
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y = 3x + 4
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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