Solve dx=-d(5x-2)

$$d x = - d ( 5 x - 2 )$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=\frac{1}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -d by 5x-2.

$$dx=5\left(-d\right)x-2\left(-d\right)$$

Multiply -2 and -1 to get 2.

$$dx=5\left(-d\right)x+2d$$

Subtract 5\left(-d\right)x from both sides.

$$dx-5\left(-d\right)x=2d$$

Subtract 2d from both sides.

$$dx-5\left(-d\right)x-2d=0$$

Multiply -1 and 5 to get -5.

$$dx-5\left(-1\right)dx-2d=0$$

Multiply -5 and -1 to get 5.

$$dx+5dx-2d=0$$

Combine dx and 5dx to get 6dx.

$$6dx-2d=0$$

Combine all terms containing d.

$$\left(6x-2\right)d=0$$

Divide 0 by 6x-2.

$$d=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{1}{3}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -d by 5x-2.

$$dx=5\left(-d\right)x-2\left(-d\right)$$

Multiply -2 and -1 to get 2.

$$dx=5\left(-d\right)x+2d$$

Subtract 5\left(-d\right)x from both sides.

$$dx-5\left(-d\right)x=2d$$

Multiply -1 and 5 to get -5.

$$dx-5\left(-1\right)dx=2d$$

Multiply -5 and -1 to get 5.

$$dx+5dx=2d$$

Combine dx and 5dx to get 6dx.

$$6dx=2d$$

Divide both sides by 6d.

$$\frac{6dx}{6d}=\frac{2d}{6d}$$

Dividing by 6d undoes the multiplication by 6d.

$$x=\frac{2d}{6d}$$

Divide 2d by 6d.

$$x=\frac{1}{3}$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&x=\frac{1}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -d by 5x-2.

$$dx=5\left(-d\right)x-2\left(-d\right)$$

Multiply -2 and -1 to get 2.

$$dx=5\left(-d\right)x+2d$$

Subtract 5\left(-d\right)x from both sides.

$$dx-5\left(-d\right)x=2d$$

Subtract 2d from both sides.

$$dx-5\left(-d\right)x-2d=0$$

Multiply -1 and 5 to get -5.

$$dx-5\left(-1\right)dx-2d=0$$

Multiply -5 and -1 to get 5.

$$dx+5dx-2d=0$$

Combine dx and 5dx to get 6dx.

$$6dx-2d=0$$

Combine all terms containing d.

$$\left(6x-2\right)d=0$$

Divide 0 by 6x-2.

$$d=0$$

Solve for x

$$\left\{\begin{matrix}\\x=\frac{1}{3}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -d by 5x-2.

$$dx=5\left(-d\right)x-2\left(-d\right)$$

Multiply -2 and -1 to get 2.

$$dx=5\left(-d\right)x+2d$$

Subtract 5\left(-d\right)x from both sides.

$$dx-5\left(-d\right)x=2d$$

Multiply -1 and 5 to get -5.

$$dx-5\left(-1\right)dx=2d$$

Multiply -5 and -1 to get 5.

$$dx+5dx=2d$$

Combine dx and 5dx to get 6dx.

$$6dx=2d$$

Divide both sides by 6d.

$$\frac{6dx}{6d}=\frac{2d}{6d}$$

Dividing by 6d undoes the multiplication by 6d.

$$x=\frac{2d}{6d}$$

Divide 2d by 6d.

$$x=\frac{1}{3}$$