Solve 7x+14z+z(5-x)+4xz=10x-3(2z+x)

$$7x+14z+z(5-x)+4xz=10x-3(2z+x)$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-\frac{25}{3}\approx -8.333333333\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply z by 5-x.

$$7x+14z+5z-zx+4xz=10x-3\left(2z+x\right)$$

Combine 14z and 5z to get 19z.

$$7x+19z-zx+4xz=10x-3\left(2z+x\right)$$

Combine -zx and 4xz to get 3zx.

$$7x+19z+3zx=10x-3\left(2z+x\right)$$

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

$$7x+19z+3zx=10x-6z-3x$$

Combine 10x and -3x to get 7x.

$$7x+19z+3zx=7x-6z$$

Subtract 7x from both sides.

$$7x+19z+3zx-7x=-6z$$

Combine 7x and -7x to get 0.

$$19z+3zx=-6z$$

Subtract 19z from both sides.

$$3zx=-6z-19z$$

Combine -6z and -19z to get -25z.

$$3zx=-25z$$

Divide both sides by 3z.

$$\frac{3zx}{3z}=-\frac{25z}{3z}$$

Dividing by 3z undoes the multiplication by 3z.

$$x=-\frac{25z}{3z}$$

Divide -25z by 3z.

$$x=-\frac{25}{3}$$

Solve for z (complex solution)

$$\left\{\begin{matrix}\\z=0\text{, }&\text{unconditionally}\\z\in \mathrm{C}\text{, }&x=-\frac{25}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply z by 5-x.

$$7x+14z+5z-zx+4xz=10x-3\left(2z+x\right)$$

Combine 14z and 5z to get 19z.

$$7x+19z-zx+4xz=10x-3\left(2z+x\right)$$

Combine -zx and 4xz to get 3zx.

$$7x+19z+3zx=10x-3\left(2z+x\right)$$

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

$$7x+19z+3zx=10x-6z-3x$$

Combine 10x and -3x to get 7x.

$$7x+19z+3zx=7x-6z$$

Add 6z to both sides.

$$7x+19z+3zx+6z=7x$$

Combine 19z and 6z to get 25z.

$$7x+25z+3zx=7x$$

Subtract 7x from both sides.

$$25z+3zx=7x-7x$$

Combine 7x and -7x to get 0.

$$25z+3zx=0$$

Combine all terms containing z.

$$\left(25+3x\right)z=0$$

The equation is in standard form.

$$\left(3x+25\right)z=0$$

Divide 0 by 25+3x.

$$z=0$$

Solve for x

$$\left\{\begin{matrix}\\x=-\frac{25}{3}\approx -8.333333333\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply z by 5-x.

$$7x+14z+5z-zx+4xz=10x-3\left(2z+x\right)$$

Combine 14z and 5z to get 19z.

$$7x+19z-zx+4xz=10x-3\left(2z+x\right)$$

Combine -zx and 4xz to get 3zx.

$$7x+19z+3zx=10x-3\left(2z+x\right)$$

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

$$7x+19z+3zx=10x-6z-3x$$

Combine 10x and -3x to get 7x.

$$7x+19z+3zx=7x-6z$$

Subtract 7x from both sides.

$$7x+19z+3zx-7x=-6z$$

Combine 7x and -7x to get 0.

$$19z+3zx=-6z$$

Subtract 19z from both sides.

$$3zx=-6z-19z$$

Combine -6z and -19z to get -25z.

$$3zx=-25z$$

Divide both sides by 3z.

$$\frac{3zx}{3z}=-\frac{25z}{3z}$$

Dividing by 3z undoes the multiplication by 3z.

$$x=-\frac{25z}{3z}$$

Divide -25z by 3z.

$$x=-\frac{25}{3}$$

Solve for z

$$\left\{\begin{matrix}\\z=0\text{, }&\text{unconditionally}\\z\in \mathrm{R}\text{, }&x=-\frac{25}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply z by 5-x.

$$7x+14z+5z-zx+4xz=10x-3\left(2z+x\right)$$

Combine 14z and 5z to get 19z.

$$7x+19z-zx+4xz=10x-3\left(2z+x\right)$$

Combine -zx and 4xz to get 3zx.

$$7x+19z+3zx=10x-3\left(2z+x\right)$$

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

$$7x+19z+3zx=10x-6z-3x$$

Combine 10x and -3x to get 7x.

$$7x+19z+3zx=7x-6z$$

Add 6z to both sides.

$$7x+19z+3zx+6z=7x$$

Combine 19z and 6z to get 25z.

$$7x+25z+3zx=7x$$

Subtract 7x from both sides.

$$25z+3zx=7x-7x$$

Combine 7x and -7x to get 0.

$$25z+3zx=0$$

Combine all terms containing z.

$$\left(25+3x\right)z=0$$

The equation is in standard form.

$$\left(3x+25\right)z=0$$

Divide 0 by 25+3x.

$$z=0$$