Solve (x-2)(x+1)=3k(4+2x)h

$$( x - 2 ) ( x + 1 ) = 3 k ( 4 + 2 x ) h$$

Solve for h (complex solution)

$$\left\{\begin{matrix}h=\frac{\left(x-2\right)\left(x+1\right)}{6k\left(x+2\right)}\text{, }&x\neq -2\text{ and }k\neq 0\\h\in \mathrm{C}\text{, }&\left(x=2\text{ or }x=-1\right)\text{ and }k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-2 by x+1 and combine like terms.

$$x^{2}-x-2=3k\left(4+2x\right)h$$

Use the distributive property to multiply 3k by 4+2x.

$$x^{2}-x-2=\left(12k+6kx\right)h$$

Use the distributive property to multiply 12k+6kx by h.

$$x^{2}-x-2=12kh+6kxh$$

Swap sides so that all variable terms are on the left hand side.

$$12kh+6kxh=x^{2}-x-2$$

Combine all terms containing h.

$$\left(12k+6kx\right)h=x^{2}-x-2$$

The equation is in standard form.

$$\left(6kx+12k\right)h=x^{2}-x-2$$

Divide both sides by 12k+6kx.

$$\frac{\left(6kx+12k\right)h}{6kx+12k}=\frac{\left(x-2\right)\left(x+1\right)}{6kx+12k}$$

Dividing by 12k+6kx undoes the multiplication by 12k+6kx.

$$h=\frac{\left(x-2\right)\left(x+1\right)}{6kx+12k}$$

Divide \left(-2+x\right)\left(1+x\right) by 12k+6kx.

$$h=\frac{\left(x-2\right)\left(x+1\right)}{6k\left(x+2\right)}$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=\frac{\left(x-2\right)\left(x+1\right)}{6h\left(x+2\right)}\text{, }&x\neq -2\text{ and }h\neq 0\\k\in \mathrm{C}\text{, }&\left(x=2\text{ or }x=-1\right)\text{ and }h=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-2 by x+1 and combine like terms.

$$x^{2}-x-2=3k\left(4+2x\right)h$$

Use the distributive property to multiply 3k by 4+2x.

$$x^{2}-x-2=\left(12k+6kx\right)h$$

Use the distributive property to multiply 12k+6kx by h.

$$x^{2}-x-2=12kh+6kxh$$

Swap sides so that all variable terms are on the left hand side.

$$12kh+6kxh=x^{2}-x-2$$

Combine all terms containing k.

$$\left(12h+6xh\right)k=x^{2}-x-2$$

The equation is in standard form.

$$\left(6hx+12h\right)k=x^{2}-x-2$$

Divide both sides by 6xh+12h.

$$\frac{\left(6hx+12h\right)k}{6hx+12h}=\frac{\left(x-2\right)\left(x+1\right)}{6hx+12h}$$

Dividing by 6xh+12h undoes the multiplication by 6xh+12h.

$$k=\frac{\left(x-2\right)\left(x+1\right)}{6hx+12h}$$

Divide \left(-2+x\right)\left(1+x\right) by 6xh+12h.

$$k=\frac{\left(x-2\right)\left(x+1\right)}{6h\left(x+2\right)}$$

Solve for h

$$\left\{\begin{matrix}h=\frac{\left(x-2\right)\left(x+1\right)}{6k\left(x+2\right)}\text{, }&x\neq -2\text{ and }k\neq 0\\h\in \mathrm{R}\text{, }&\left(x=2\text{ or }x=-1\right)\text{ and }k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-2 by x+1 and combine like terms.

$$x^{2}-x-2=3k\left(4+2x\right)h$$

Use the distributive property to multiply 3k by 4+2x.

$$x^{2}-x-2=\left(12k+6kx\right)h$$

Use the distributive property to multiply 12k+6kx by h.

$$x^{2}-x-2=12kh+6kxh$$

Swap sides so that all variable terms are on the left hand side.

$$12kh+6kxh=x^{2}-x-2$$

Combine all terms containing h.

$$\left(12k+6kx\right)h=x^{2}-x-2$$

The equation is in standard form.

$$\left(6kx+12k\right)h=x^{2}-x-2$$

Divide both sides by 12k+6kx.

$$\frac{\left(6kx+12k\right)h}{6kx+12k}=\frac{\left(x-2\right)\left(x+1\right)}{6kx+12k}$$

Dividing by 12k+6kx undoes the multiplication by 12k+6kx.

$$h=\frac{\left(x-2\right)\left(x+1\right)}{6kx+12k}$$

Divide \left(-2+x\right)\left(1+x\right) by 12k+6kx.

$$h=\frac{\left(x-2\right)\left(x+1\right)}{6k\left(x+2\right)}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{\left(x-2\right)\left(x+1\right)}{6h\left(x+2\right)}\text{, }&x\neq -2\text{ and }h\neq 0\\k\in \mathrm{R}\text{, }&\left(x=2\text{ or }x=-1\right)\text{ and }h=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-2 by x+1 and combine like terms.

$$x^{2}-x-2=3k\left(4+2x\right)h$$

Use the distributive property to multiply 3k by 4+2x.

$$x^{2}-x-2=\left(12k+6kx\right)h$$

Use the distributive property to multiply 12k+6kx by h.

$$x^{2}-x-2=12kh+6kxh$$

Swap sides so that all variable terms are on the left hand side.

$$12kh+6kxh=x^{2}-x-2$$

Combine all terms containing k.

$$\left(12h+6xh\right)k=x^{2}-x-2$$

The equation is in standard form.

$$\left(6hx+12h\right)k=x^{2}-x-2$$

Divide both sides by 6xh+12h.

$$\frac{\left(6hx+12h\right)k}{6hx+12h}=\frac{\left(x-2\right)\left(x+1\right)}{6hx+12h}$$

Dividing by 6xh+12h undoes the multiplication by 6xh+12h.

$$k=\frac{\left(x-2\right)\left(x+1\right)}{6hx+12h}$$

Divide \left(-2+x\right)\left(1+x\right) by 6xh+12h.

$$k=\frac{\left(x-2\right)\left(x+1\right)}{6h\left(x+2\right)}$$