d x = d ( 7 x - 3 )
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=7dx-3d
Use the distributive property to multiply d by 7x-3.
dx-7dx=-3d
Subtract 7dx from both sides.
-6dx=-3d
Combine dx and -7dx to get -6dx.
-6dx+3d=0
Add 3d to both sides.
\left(-6x+3\right)d=0
Combine all terms containing d.
\left(3-6x\right)d=0
The equation is in standard form.
d=0
Divide 0 by -6x+3.
dx=7dx-3d
Use the distributive property to multiply d by 7x-3.
dx-7dx=-3d
Subtract 7dx from both sides.
-6dx=-3d
Combine dx and -7dx to get -6dx.
\left(-6d\right)x=-3d
The equation is in standard form.
\frac{\left(-6d\right)x}{-6d}=-\frac{3d}{-6d}
Divide both sides by -6d.
x=-\frac{3d}{-6d}
Dividing by -6d undoes the multiplication by -6d.
x=\frac{1}{2}
Divide -3d by -6d.
dx=7dx-3d
Use the distributive property to multiply d by 7x-3.
dx-7dx=-3d
Subtract 7dx from both sides.
-6dx=-3d
Combine dx and -7dx to get -6dx.
-6dx+3d=0
Add 3d to both sides.
\left(-6x+3\right)d=0
Combine all terms containing d.
\left(3-6x\right)d=0
The equation is in standard form.
d=0
Divide 0 by -6x+3.
dx=7dx-3d
Use the distributive property to multiply d by 7x-3.
dx-7dx=-3d
Subtract 7dx from both sides.
-6dx=-3d
Combine dx and -7dx to get -6dx.
\left(-6d\right)x=-3d
The equation is in standard form.
\frac{\left(-6d\right)x}{-6d}=-\frac{3d}{-6d}
Divide both sides by -6d.
x=-\frac{3d}{-6d}
Dividing by -6d undoes the multiplication by -6d.
x=\frac{1}{2}
Divide -3d by -6d.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
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699 * 533
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}