Solve 0=-x^7-2yx^5-yx^4+1.5x^2+9/8

$$0=- { x }^{ 7 } -2y { x }^{ 5 } -y { x }^{ 4 } +1.5 { x }^{ 2 } + \frac{ 9 }{ 8 }$$

Solve for y

$$y=\frac{9+12x^{2}-8x^{7}}{8\left(2x+1\right)x^{4}}$$

$$x\neq 0\text{ and }x\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

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

$$-x^{7}-2yx^{5}-yx^{4}+1.5x^{2}+\frac{9}{8}=0$$

Subtract 1.5x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-x^{7}-2yx^{5}-yx^{4}+\frac{9}{8}=-1.5x^{2}$$

Subtract \frac{9}{8} from both sides.

$$-x^{7}-2yx^{5}-yx^{4}=-1.5x^{2}-\frac{9}{8}$$

Add x^{7} to both sides.

$$-2yx^{5}-yx^{4}=-1.5x^{2}-\frac{9}{8}+x^{7}$$

Combine all terms containing y.

$$\left(-2x^{5}-x^{4}\right)y=-1.5x^{2}-\frac{9}{8}+x^{7}$$

The equation is in standard form.

$$\left(-2x^{5}-x^{4}\right)y=x^{7}-\frac{3x^{2}}{2}-\frac{9}{8}$$

Divide both sides by -2x^{5}-x^{4}.

$$\frac{\left(-2x^{5}-x^{4}\right)y}{-2x^{5}-x^{4}}=\frac{x^{7}-\frac{3x^{2}}{2}-\frac{9}{8}}{-2x^{5}-x^{4}}$$

Dividing by -2x^{5}-x^{4} undoes the multiplication by -2x^{5}-x^{4}.

$$y=\frac{x^{7}-\frac{3x^{2}}{2}-\frac{9}{8}}{-2x^{5}-x^{4}}$$

Divide -\frac{3x^{2}}{2}-\frac{9}{8}+x^{7} by -2x^{5}-x^{4}.

$$y=-\frac{8x^{7}-12x^{2}-9}{8\left(2x+1\right)x^{4}}$$