Solve for g (complex solution)
\left\{\begin{matrix}g=-\frac{2x+3}{kx}\text{, }&x\neq 0\text{ and }k\neq 0\\g\in \mathrm{C}\text{, }&x=-\frac{3}{2}\text{ and }k=0\end{matrix}\right.
Solve for k (complex solution)
\left\{\begin{matrix}k=-\frac{2x+3}{gx}\text{, }&x\neq 0\text{ and }g\neq 0\\k\in \mathrm{C}\text{, }&x=-\frac{3}{2}\text{ and }g=0\end{matrix}\right.
Solve for g
\left\{\begin{matrix}g=-\frac{2x+3}{kx}\text{, }&x\neq 0\text{ and }k\neq 0\\g\in \mathrm{R}\text{, }&x=-\frac{3}{2}\text{ and }k=0\end{matrix}\right.
Solve for k
\left\{\begin{matrix}k=-\frac{2x+3}{gx}\text{, }&x\neq 0\text{ and }g\neq 0\\k\in \mathrm{R}\text{, }&x=-\frac{3}{2}\text{ and }g=0\end{matrix}\right.
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-kgx=4x+3-2x
Subtract 2x from both sides.
-kgx=2x+3
Combine 4x and -2x to get 2x.
\left(-kx\right)g=2x+3
The equation is in standard form.
\frac{\left(-kx\right)g}{-kx}=\frac{2x+3}{-kx}
Divide both sides by -kx.
g=\frac{2x+3}{-kx}
Dividing by -kx undoes the multiplication by -kx.
g=-\frac{2x+3}{kx}
Divide 2x+3 by -kx.
-kgx=4x+3-2x
Subtract 2x from both sides.
-kgx=2x+3
Combine 4x and -2x to get 2x.
\left(-gx\right)k=2x+3
The equation is in standard form.
\frac{\left(-gx\right)k}{-gx}=\frac{2x+3}{-gx}
Divide both sides by -gx.
k=\frac{2x+3}{-gx}
Dividing by -gx undoes the multiplication by -gx.
k=-\frac{2x+3}{gx}
Divide 2x+3 by -gx.
-kgx=4x+3-2x
Subtract 2x from both sides.
-kgx=2x+3
Combine 4x and -2x to get 2x.
\left(-kx\right)g=2x+3
The equation is in standard form.
\frac{\left(-kx\right)g}{-kx}=\frac{2x+3}{-kx}
Divide both sides by -kx.
g=\frac{2x+3}{-kx}
Dividing by -kx undoes the multiplication by -kx.
g=-\frac{2x+3}{kx}
Divide 2x+3 by -kx.
-kgx=4x+3-2x
Subtract 2x from both sides.
-kgx=2x+3
Combine 4x and -2x to get 2x.
\left(-gx\right)k=2x+3
The equation is in standard form.
\frac{\left(-gx\right)k}{-gx}=\frac{2x+3}{-gx}
Divide both sides by -gx.
k=\frac{2x+3}{-gx}
Dividing by -gx undoes the multiplication by -gx.
k=-\frac{2x+3}{gx}
Divide 2x+3 by -gx.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
Arithmetic
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}