Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{4c}{3\left(5b+1\right)}\text{, }&b\neq -\frac{1}{5}\\a\in \mathrm{C}\text{, }&c=0\text{ and }b=-\frac{1}{5}\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=\frac{4c}{15a}-\frac{1}{5}\text{, }&a\neq 0\\b\in \mathrm{C}\text{, }&a=0\text{ and }c=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{4c}{3\left(5b+1\right)}\text{, }&b\neq -\frac{1}{5}\\a\in \mathrm{R}\text{, }&c=0\text{ and }b=-\frac{1}{5}\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=\frac{4c}{15a}-\frac{1}{5}\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&a=0\text{ and }c=0\end{matrix}\right.
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3a+15ba=4c
Multiply 5 and 3 to get 15.
\left(3+15b\right)a=4c
Combine all terms containing a.
\left(15b+3\right)a=4c
The equation is in standard form.
\frac{\left(15b+3\right)a}{15b+3}=\frac{4c}{15b+3}
Divide both sides by 15b+3.
a=\frac{4c}{15b+3}
Dividing by 15b+3 undoes the multiplication by 15b+3.
a=\frac{4c}{3\left(5b+1\right)}
Divide 4c by 15b+3.
3a+15ba=4c
Multiply 5 and 3 to get 15.
15ba=4c-3a
Subtract 3a from both sides.
15ab=4c-3a
The equation is in standard form.
\frac{15ab}{15a}=\frac{4c-3a}{15a}
Divide both sides by 15a.
b=\frac{4c-3a}{15a}
Dividing by 15a undoes the multiplication by 15a.
b=\frac{4c}{15a}-\frac{1}{5}
Divide 4c-3a by 15a.
3a+15ba=4c
Multiply 5 and 3 to get 15.
\left(3+15b\right)a=4c
Combine all terms containing a.
\left(15b+3\right)a=4c
The equation is in standard form.
\frac{\left(15b+3\right)a}{15b+3}=\frac{4c}{15b+3}
Divide both sides by 15b+3.
a=\frac{4c}{15b+3}
Dividing by 15b+3 undoes the multiplication by 15b+3.
a=\frac{4c}{3\left(5b+1\right)}
Divide 4c by 15b+3.
3a+15ba=4c
Multiply 5 and 3 to get 15.
15ba=4c-3a
Subtract 3a from both sides.
15ab=4c-3a
The equation is in standard form.
\frac{15ab}{15a}=\frac{4c-3a}{15a}
Divide both sides by 15a.
b=\frac{4c-3a}{15a}
Dividing by 15a undoes the multiplication by 15a.
b=\frac{4c}{15a}-\frac{1}{5}
Divide 4c-3a by 15a.
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}