Solve h(x)=(x-1,5)(x+1,5)x

$$h ( x ) = ( x - 1,5 ) ( x + 1,5 ) x$$

Solve for h

$$\left\{\begin{matrix}\\h=x^{2}-2,25\text{, }&\text{unconditionally}\\h\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-1,5 by x+1,5 and combine like terms.

$$hx=\left(x^{2}-2,25\right)x$$

Use the distributive property to multiply x^{2}-2,25 by x.

$$hx=x^{3}-2,25x$$

The equation is in standard form.

$$xh=x^{3}-\frac{9x}{4}$$

Divide both sides by x.

$$\frac{xh}{x}=\frac{x^{3}-\frac{9x}{4}}{x}$$

Dividing by x undoes the multiplication by x.

$$h=\frac{x^{3}-\frac{9x}{4}}{x}$$

Divide x^{3}-\frac{9x}{4} by x.

$$h=x^{2}-\frac{9}{4}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{\sqrt{4h+9}}{2}\text{; }x=-\frac{\sqrt{4h+9}}{2}\text{, }&h\geq -\frac{9}{4}\end{matrix}\right.$$