Solve 5h+2x(3+2y/y+3)=4

$$5 h + 2 x ( \frac { 3 + 2 y } { y + 3 } ) = 4$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\left(5h-4\right)\left(y+3\right)}{2\left(2y+3\right)}\text{, }&y\neq -\frac{3}{2}\text{ and }y\neq -3\\x\in \mathrm{C}\text{, }&y=-\frac{3}{2}\text{ and }h=\frac{4}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y+3.

$$5h\left(y+3\right)+2x\left(3+2y\right)=4\left(y+3\right)$$

Use the distributive property to multiply 5h by y+3.

$$5hy+15h+2x\left(3+2y\right)=4\left(y+3\right)$$

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

$$5hy+15h+6x+4xy=4\left(y+3\right)$$

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

$$5hy+15h+6x+4xy=4y+12$$

Subtract 5hy from both sides.

$$15h+6x+4xy=4y+12-5hy$$

Subtract 15h from both sides.

$$6x+4xy=4y+12-5hy-15h$$

Combine all terms containing x.

$$\left(6+4y\right)x=4y+12-5hy-15h$$

The equation is in standard form.

$$\left(4y+6\right)x=12-15h+4y-5hy$$

Divide both sides by 4y+6.

$$\frac{\left(4y+6\right)x}{4y+6}=\frac{\left(4-5h\right)\left(y+3\right)}{4y+6}$$

Dividing by 4y+6 undoes the multiplication by 4y+6.

$$x=\frac{\left(4-5h\right)\left(y+3\right)}{4y+6}$$

Divide \left(3+y\right)\left(4-5h\right) by 4y+6.

$$x=\frac{\left(4-5h\right)\left(y+3\right)}{2\left(2y+3\right)}$$

Solve for h

$$h=-\frac{2\left(2xy+3x-2y-6\right)}{5\left(y+3\right)}$$

$$y\neq -3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y+3.

$$5h\left(y+3\right)+2x\left(3+2y\right)=4\left(y+3\right)$$

Use the distributive property to multiply 5h by y+3.

$$5hy+15h+2x\left(3+2y\right)=4\left(y+3\right)$$

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

$$5hy+15h+6x+4xy=4\left(y+3\right)$$

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

$$5hy+15h+6x+4xy=4y+12$$

Subtract 6x from both sides.

$$5hy+15h+4xy=4y+12-6x$$

Subtract 4xy from both sides.

$$5hy+15h=4y+12-6x-4xy$$

Combine all terms containing h.

$$\left(5y+15\right)h=4y+12-6x-4xy$$

The equation is in standard form.

$$\left(5y+15\right)h=12+4y-6x-4xy$$

Divide both sides by 5y+15.

$$\frac{\left(5y+15\right)h}{5y+15}=\frac{12+4y-6x-4xy}{5y+15}$$

Dividing by 5y+15 undoes the multiplication by 5y+15.

$$h=\frac{12+4y-6x-4xy}{5y+15}$$

Divide 4y+12-6x-4xy by 5y+15.

$$h=\frac{2\left(6+2y-3x-2xy\right)}{5\left(y+3\right)}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\left(5h-4\right)\left(y+3\right)}{2\left(2y+3\right)}\text{, }&y\neq -\frac{3}{2}\text{ and }y\neq -3\\x\in \mathrm{R}\text{, }&y=-\frac{3}{2}\text{ and }h=\frac{4}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y+3.

$$5h\left(y+3\right)+2x\left(3+2y\right)=4\left(y+3\right)$$

Use the distributive property to multiply 5h by y+3.

$$5hy+15h+2x\left(3+2y\right)=4\left(y+3\right)$$

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

$$5hy+15h+6x+4xy=4\left(y+3\right)$$

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

$$5hy+15h+6x+4xy=4y+12$$

Subtract 5hy from both sides.

$$15h+6x+4xy=4y+12-5hy$$

Subtract 15h from both sides.

$$6x+4xy=4y+12-5hy-15h$$

Combine all terms containing x.

$$\left(6+4y\right)x=4y+12-5hy-15h$$

The equation is in standard form.

$$\left(4y+6\right)x=12-15h+4y-5hy$$

Divide both sides by 4y+6.

$$\frac{\left(4y+6\right)x}{4y+6}=\frac{\left(4-5h\right)\left(y+3\right)}{4y+6}$$

Dividing by 4y+6 undoes the multiplication by 4y+6.

$$x=\frac{\left(4-5h\right)\left(y+3\right)}{4y+6}$$

Divide \left(3+y\right)\left(4-5h\right) by 4y+6.

$$x=\frac{\left(4-5h\right)\left(y+3\right)}{2\left(2y+3\right)}$$