Solve z=2x+y-4x^2/2x+11[x]

$$z = 2 x + y - \frac { 4 x ^ { 2 } } { 2 x + 11 } [ x ]$$

Solve for y

$$y=-\frac{-4x^{3}+4x^{2}-2xz+22x-11z}{2x+11}$$

$$x\neq -\frac{11}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x+11.

$$z\left(2x+11\right)=\left(2x+11\right)\left(2x+y\right)-4x^{2}x$$

Use the distributive property to multiply z by 2x+11.

$$2zx+11z=\left(2x+11\right)\left(2x+y\right)-4x^{2}x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$2zx+11z=\left(2x+11\right)\left(2x+y\right)-4x^{3}$$

Use the distributive property to multiply 2x+11 by 2x+y.

$$2zx+11z=4x^{2}+2xy+22x+11y-4x^{3}$$

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

$$4x^{2}+2xy+22x+11y-4x^{3}=2zx+11z$$

Subtract 4x^{2} from both sides.

$$2xy+22x+11y-4x^{3}=2zx+11z-4x^{2}$$

Subtract 22x from both sides.

$$2xy+11y-4x^{3}=2zx+11z-4x^{2}-22x$$

Add 4x^{3} to both sides.

$$2xy+11y=2zx+11z-4x^{2}-22x+4x^{3}$$

Combine all terms containing y.

$$\left(2x+11\right)y=2zx+11z-4x^{2}-22x+4x^{3}$$

The equation is in standard form.

$$\left(2x+11\right)y=4x^{3}-4x^{2}+2xz-22x+11z$$

Divide both sides by 2x+11.

$$\frac{\left(2x+11\right)y}{2x+11}=\frac{4x^{3}-4x^{2}+2xz-22x+11z}{2x+11}$$

Dividing by 2x+11 undoes the multiplication by 2x+11.

$$y=\frac{4x^{3}-4x^{2}+2xz-22x+11z}{2x+11}$$