Solve dy/dx=(3x-2)(2y+1)

$$d y / d x = ( 3 x - 2 ) ( 2 y + 1 )$$

Solve for d

$$d\neq 0$$

$$y=-\frac{2-3x}{4-5x}\text{ and }x\neq \frac{4}{5}$$

Steps for Solving Linear Equation

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by d.

$$dyx=\left(3x-2\right)\left(2y+1\right)d$$

Use the distributive property to multiply 3x-2 by 2y+1.

$$dyx=\left(6xy+3x-4y-2\right)d$$

Use the distributive property to multiply 6xy+3x-4y-2 by d.

$$dyx=6xyd+3xd-4yd-2d$$

Subtract 6xyd from both sides.

$$dyx-6xyd=3xd-4yd-2d$$

Combine dyx and -6xyd to get -5dyx.

$$-5dyx=3xd-4yd-2d$$

Subtract 3xd from both sides.

$$-5dyx-3xd=-4yd-2d$$

Add 4yd to both sides.

$$-5dyx-3xd+4yd=-2d$$

Add 2d to both sides.

$$-5dyx-3xd+4yd+2d=0$$

Combine all terms containing d.

$$\left(-5yx-3x+4y+2\right)d=0$$

The equation is in standard form.

$$\left(2+4y-3x-5xy\right)d=0$$

Divide 0 by -5yx-3x+4y+2.

$$d=0$$

Variable d cannot be equal to 0.

$$d\in \emptyset$$

Solve for x

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

$$y\neq -\frac{3}{5}\text{ and }d\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by d.

$$dyx=\left(3x-2\right)\left(2y+1\right)d$$

Use the distributive property to multiply 3x-2 by 2y+1.

$$dyx=\left(6xy+3x-4y-2\right)d$$

Use the distributive property to multiply 6xy+3x-4y-2 by d.

$$dyx=6xyd+3xd-4yd-2d$$

Subtract 6xyd from both sides.

$$dyx-6xyd=3xd-4yd-2d$$

Combine dyx and -6xyd to get -5dyx.

$$-5dyx=3xd-4yd-2d$$

Subtract 3xd from both sides.

$$-5dyx-3xd=-4yd-2d$$

Combine all terms containing x.

$$\left(-5dy-3d\right)x=-4yd-2d$$

The equation is in standard form.

$$\left(-5dy-3d\right)x=-4dy-2d$$

Divide both sides by -5dy-3d.

$$\frac{\left(-5dy-3d\right)x}{-5dy-3d}=\frac{-4dy-2d}{-5dy-3d}$$

Dividing by -5dy-3d undoes the multiplication by -5dy-3d.

$$x=\frac{-4dy-2d}{-5dy-3d}$$

Divide -2d-4dy by -5dy-3d.

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