d x = d ( 5 x - 2 )
Solve for d (complex solution)
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=\frac{1}{2}\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=\frac{1}{2}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.
Solve for d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&x=\frac{1}{2}\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=\frac{1}{2}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.
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dx=5dx-2d
Use the distributive property to multiply d by 5x-2.
dx-5dx=-2d
Subtract 5dx from both sides.
-4dx=-2d
Combine dx and -5dx to get -4dx.
-4dx+2d=0
Add 2d to both sides.
\left(-4x+2\right)d=0
Combine all terms containing d.
\left(2-4x\right)d=0
The equation is in standard form.
d=0
Divide 0 by -4x+2.
dx=5dx-2d
Use the distributive property to multiply d by 5x-2.
dx-5dx=-2d
Subtract 5dx from both sides.
-4dx=-2d
Combine dx and -5dx to get -4dx.
\left(-4d\right)x=-2d
The equation is in standard form.
\frac{\left(-4d\right)x}{-4d}=-\frac{2d}{-4d}
Divide both sides by -4d.
x=-\frac{2d}{-4d}
Dividing by -4d undoes the multiplication by -4d.
x=\frac{1}{2}
Divide -2d by -4d.
dx=5dx-2d
Use the distributive property to multiply d by 5x-2.
dx-5dx=-2d
Subtract 5dx from both sides.
-4dx=-2d
Combine dx and -5dx to get -4dx.
-4dx+2d=0
Add 2d to both sides.
\left(-4x+2\right)d=0
Combine all terms containing d.
\left(2-4x\right)d=0
The equation is in standard form.
d=0
Divide 0 by -4x+2.
dx=5dx-2d
Use the distributive property to multiply d by 5x-2.
dx-5dx=-2d
Subtract 5dx from both sides.
-4dx=-2d
Combine dx and -5dx to get -4dx.
\left(-4d\right)x=-2d
The equation is in standard form.
\frac{\left(-4d\right)x}{-4d}=-\frac{2d}{-4d}
Divide both sides by -4d.
x=-\frac{2d}{-4d}
Dividing by -4d undoes the multiplication by -4d.
x=\frac{1}{2}
Divide -2d by -4d.
Examples
Quadratic equation
{ 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}