Solve (-3+y)*(2+x)=(4+y)*(-3+x)

$$( - 3 + y ) \cdot ( 2 + x ) = ( 4 + y ) \cdot ( - 3 + x )$$

Solve for x

$$x=\frac{5y+6}{7}$$

Steps for Solving Linear Equation

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

$$-6-3x+2y+yx=\left(4+y\right)\left(-3+x\right)$$

Use the distributive property to multiply 4+y by -3+x.

$$-6-3x+2y+yx=-12+4x-3y+yx$$

Subtract 4x from both sides.

$$-6-3x+2y+yx-4x=-12-3y+yx$$

Combine -3x and -4x to get -7x.

$$-6-7x+2y+yx=-12-3y+yx$$

Subtract yx from both sides.

$$-6-7x+2y+yx-yx=-12-3y$$

Combine yx and -yx to get 0.

$$-6-7x+2y=-12-3y$$

Add 6 to both sides.

$$-7x+2y=-12-3y+6$$

Add -12 and 6 to get -6.

$$-7x+2y=-6-3y$$

Subtract 2y from both sides.

$$-7x=-6-3y-2y$$

Combine -3y and -2y to get -5y.

$$-7x=-6-5y$$

The equation is in standard form.

$$-7x=-5y-6$$

Divide both sides by -7.

$$\frac{-7x}{-7}=\frac{-5y-6}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$x=\frac{-5y-6}{-7}$$

Divide -6-5y by -7.

$$x=\frac{5y+6}{7}$$

Solve for y

$$y=\frac{7x-6}{5}$$

Steps for Solving Linear Equation

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

$$-6-3x+2y+yx=\left(4+y\right)\left(-3+x\right)$$

Use the distributive property to multiply 4+y by -3+x.

$$-6-3x+2y+yx=-12+4x-3y+yx$$

Add 3y to both sides.

$$-6-3x+2y+yx+3y=-12+4x+yx$$

Combine 2y and 3y to get 5y.

$$-6-3x+5y+yx=-12+4x+yx$$

Subtract yx from both sides.

$$-6-3x+5y+yx-yx=-12+4x$$

Combine yx and -yx to get 0.

$$-6-3x+5y=-12+4x$$

Add 6 to both sides.

$$-3x+5y=-12+4x+6$$

Add -12 and 6 to get -6.

$$-3x+5y=-6+4x$$

Add 3x to both sides.

$$5y=-6+4x+3x$$

Combine 4x and 3x to get 7x.

$$5y=-6+7x$$

The equation is in standard form.

$$5y=7x-6$$

Divide both sides by 5.

$$\frac{5y}{5}=\frac{7x-6}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$y=\frac{7x-6}{5}$$