Solve 4x(4-y)=3x(y-3)

$$4 x ( 4 - y ) = 3 x ( y - 3 )$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=\frac{25}{7}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$16x-4xy=3x\left(y-3\right)$$

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

$$16x-4xy=3xy-9x$$

Subtract 3xy from both sides.

$$16x-4xy-3xy=-9x$$

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

$$16x-7xy=-9x$$

Add 9x to both sides.

$$16x-7xy+9x=0$$

Combine 16x and 9x to get 25x.

$$25x-7xy=0$$

Combine all terms containing x.

$$\left(25-7y\right)x=0$$

Divide 0 by 25-7y.

$$x=0$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=\frac{25}{7}\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$16x-4xy=3x\left(y-3\right)$$

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

$$16x-4xy=3xy-9x$$

Subtract 3xy from both sides.

$$16x-4xy-3xy=-9x$$

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

$$16x-7xy=-9x$$

Subtract 16x from both sides.

$$-7xy=-9x-16x$$

Combine -9x and -16x to get -25x.

$$-7xy=-25x$$

The equation is in standard form.

$$\left(-7x\right)y=-25x$$

Divide both sides by -7x.

$$\frac{\left(-7x\right)y}{-7x}=-\frac{25x}{-7x}$$

Dividing by -7x undoes the multiplication by -7x.

$$y=-\frac{25x}{-7x}$$

Divide -25x by -7x.

$$y=\frac{25}{7}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=\frac{25}{7}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$16x-4xy=3x\left(y-3\right)$$

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

$$16x-4xy=3xy-9x$$

Subtract 3xy from both sides.

$$16x-4xy-3xy=-9x$$

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

$$16x-7xy=-9x$$

Add 9x to both sides.

$$16x-7xy+9x=0$$

Combine 16x and 9x to get 25x.

$$25x-7xy=0$$

Combine all terms containing x.

$$\left(25-7y\right)x=0$$

Divide 0 by 25-7y.

$$x=0$$

Solve for y

$$\left\{\begin{matrix}\\y=\frac{25}{7}\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$16x-4xy=3x\left(y-3\right)$$

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

$$16x-4xy=3xy-9x$$

Subtract 3xy from both sides.

$$16x-4xy-3xy=-9x$$

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

$$16x-7xy=-9x$$

Subtract 16x from both sides.

$$-7xy=-9x-16x$$

Combine -9x and -16x to get -25x.

$$-7xy=-25x$$

The equation is in standard form.

$$\left(-7x\right)y=-25x$$

Divide both sides by -7x.

$$\frac{\left(-7x\right)y}{-7x}=-\frac{25x}{-7x}$$

Dividing by -7x undoes the multiplication by -7x.

$$y=-\frac{25x}{-7x}$$

Divide -25x by -7x.

$$y=\frac{25}{7}$$