Solve f(x)=-2x(x+1)(x-2,5)

$$f ( x ) = - 2 x ( x + 1 ) ( x - 2,5 )$$

Solve for f

$$\left\{\begin{matrix}\\f=-2\left(x-2,5\right)\left(x+1\right)\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2x by x+1.

$$fx=\left(-2x^{2}-2x\right)\left(x-2,5\right)$$

Use the distributive property to multiply -2x^{2}-2x by x-2,5 and combine like terms.

$$fx=-2x^{3}+3x^{2}+5x$$

The equation is in standard form.

$$xf=5x+3x^{2}-2x^{3}$$

Divide both sides by x.

$$\frac{xf}{x}=-\frac{x\left(2x-5\right)\left(x+1\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$f=-\frac{x\left(2x-5\right)\left(x+1\right)}{x}$$

Divide -x\left(-5+2x\right)\left(1+x\right) by x.

$$f=-\left(2x-5\right)\left(x+1\right)$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{\sqrt{49-8f}+3}{4}\text{; }x=\frac{-\sqrt{49-8f}+3}{4}\text{, }&f\leq \frac{49}{8}\end{matrix}\right.$$