Solve for g (complex solution)
\left\{\begin{matrix}g=\frac{2\left(x-2\right)}{y}\text{, }&y\neq 0\\g\in \mathrm{C}\text{, }&x=0\text{ or }\left(x=2\text{ and }y=0\right)\end{matrix}\right.
Solve for g
\left\{\begin{matrix}g=\frac{2\left(x-2\right)}{y}\text{, }&y\neq 0\\g\in \mathrm{R}\text{, }&x=0\text{ or }\left(x=2\text{ and }y=0\right)\end{matrix}\right.
Solve for x
x=\frac{gy+4}{2}
x=0
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-5x-2ygx=3x-4x^{2}
Subtract 4x^{2} from both sides.
-2ygx=3x-4x^{2}+5x
Add 5x to both sides.
-2ygx=8x-4x^{2}
Combine 3x and 5x to get 8x.
\left(-2xy\right)g=8x-4x^{2}
The equation is in standard form.
\frac{\left(-2xy\right)g}{-2xy}=\frac{4x\left(2-x\right)}{-2xy}
Divide both sides by -2yx.
g=\frac{4x\left(2-x\right)}{-2xy}
Dividing by -2yx undoes the multiplication by -2yx.
g=-\frac{2\left(2-x\right)}{y}
Divide 4x\left(2-x\right) by -2yx.
-5x-2ygx=3x-4x^{2}
Subtract 4x^{2} from both sides.
-2ygx=3x-4x^{2}+5x
Add 5x to both sides.
-2ygx=8x-4x^{2}
Combine 3x and 5x to get 8x.
\left(-2xy\right)g=8x-4x^{2}
The equation is in standard form.
\frac{\left(-2xy\right)g}{-2xy}=\frac{4x\left(2-x\right)}{-2xy}
Divide both sides by -2yx.
g=\frac{4x\left(2-x\right)}{-2xy}
Dividing by -2yx undoes the multiplication by -2yx.
g=-\frac{2\left(2-x\right)}{y}
Divide 4x\left(2-x\right) by -2yx.
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}