Solve for T (complex solution)
\left\{\begin{matrix}T=-\frac{xz-2yz-y-z}{4y}\text{, }&y\neq 0\\T\in \mathrm{C}\text{, }&\left(z=0\text{ or }x=1\right)\text{ and }y=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{2yz-4Ty+y+z}{z}\text{, }&z\neq 0\\x\in \mathrm{C}\text{, }&\left(y=0\text{ or }T=\frac{1}{4}\right)\text{ and }z=0\end{matrix}\right.
Solve for T
\left\{\begin{matrix}T=-\frac{xz-2yz-y-z}{4y}\text{, }&y\neq 0\\T\in \mathrm{R}\text{, }&\left(z=0\text{ or }x=1\right)\text{ and }y=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{2yz-4Ty+y+z}{z}\text{, }&z\neq 0\\x\in \mathrm{R}\text{, }&\left(y=0\text{ or }T=\frac{1}{4}\right)\text{ and }z=0\end{matrix}\right.
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xz-2y\left(z-2T\right)=z+y
Multiply -1 and 2 to get -2.
xz-2yz+4yT=z+y
Use the distributive property to multiply -2y by z-2T.
-2yz+4yT=z+y-xz
Subtract xz from both sides.
4yT=z+y-xz+2yz
Add 2yz to both sides.
4yT=z+y+2yz-xz
The equation is in standard form.
\frac{4yT}{4y}=\frac{z+y+2yz-xz}{4y}
Divide both sides by 4y.
T=\frac{z+y+2yz-xz}{4y}
Dividing by 4y undoes the multiplication by 4y.
xz=z+y+2y\left(z-2T\right)
Add 2y\left(z-2T\right) to both sides.
xz=z+y+2yz-4Ty
Use the distributive property to multiply 2y by z-2T.
zx=2yz-4Ty+y+z
The equation is in standard form.
\frac{zx}{z}=\frac{2yz-4Ty+y+z}{z}
Divide both sides by z.
x=\frac{2yz-4Ty+y+z}{z}
Dividing by z undoes the multiplication by z.
xz-2y\left(z-2T\right)=z+y
Multiply -1 and 2 to get -2.
xz-2yz+4yT=z+y
Use the distributive property to multiply -2y by z-2T.
-2yz+4yT=z+y-xz
Subtract xz from both sides.
4yT=z+y-xz+2yz
Add 2yz to both sides.
4yT=z+y+2yz-xz
The equation is in standard form.
\frac{4yT}{4y}=\frac{z+y+2yz-xz}{4y}
Divide both sides by 4y.
T=\frac{z+y+2yz-xz}{4y}
Dividing by 4y undoes the multiplication by 4y.
xz=z+y+2y\left(z-2T\right)
Add 2y\left(z-2T\right) to both sides.
xz=z+y+2yz-4Ty
Use the distributive property to multiply 2y by z-2T.
zx=2yz-4Ty+y+z
The equation is in standard form.
\frac{zx}{z}=\frac{2yz-4Ty+y+z}{z}
Divide both sides by z.
x=\frac{2yz-4Ty+y+z}{z}
Dividing by z undoes the multiplication by z.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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}