Solve (x-2)=pm3(2x+5)

$$( x - 2 ) = \pm 3 ( 2 x + 5 )$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

$$-5\left(±3\right)-2=0\text{ and }-2\left(±3\right)+1=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply ±3 by 2x+5.

$$x-2=2\left(±3\right)x+5\left(±3\right)$$

Subtract 2\left(±3\right)x from both sides.

$$x-2-2\left(±3\right)x=5\left(±3\right)$$

Add 2 to both sides.

$$x-2\left(±3\right)x=5\left(±3\right)+2$$

Combine all terms containing x.

$$\left(1-2\left(±3\right)\right)x=5\left(±3\right)+2$$

The equation is in standard form.

$$\left(-2\left(±3\right)+1\right)x=5\left(±3\right)+2$$

Divide both sides by 1-2\left(±3\right).

$$\frac{\left(-2\left(±3\right)+1\right)x}{-2\left(±3\right)+1}=\frac{5\left(±3\right)+2}{-2\left(±3\right)+1}$$

Dividing by 1-2\left(±3\right) undoes the multiplication by 1-2\left(±3\right).

$$x=\frac{5\left(±3\right)+2}{-2\left(±3\right)+1}$$

Solve for x

$$x\in \mathrm{R}$$

$$-5\left(±3\right)-2=0\text{ and }-2\left(±3\right)+1=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply ±3 by 2x+5.

$$x-2=2\left(±3\right)x+5\left(±3\right)$$

Subtract 2\left(±3\right)x from both sides.

$$x-2-2\left(±3\right)x=5\left(±3\right)$$

Add 2 to both sides.

$$x-2\left(±3\right)x=5\left(±3\right)+2$$

Combine all terms containing x.

$$\left(1-2\left(±3\right)\right)x=5\left(±3\right)+2$$

The equation is in standard form.

$$\left(-2\left(±3\right)+1\right)x=5\left(±3\right)+2$$

Divide both sides by 1-2\left(±3\right).

$$\frac{\left(-2\left(±3\right)+1\right)x}{-2\left(±3\right)+1}=\frac{5\left(±3\right)+2}{-2\left(±3\right)+1}$$

Dividing by 1-2\left(±3\right) undoes the multiplication by 1-2\left(±3\right).

$$x=\frac{5\left(±3\right)+2}{-2\left(±3\right)+1}$$