Solve x^3-mx^2+3x-2=0

$$x ^ { 3 } - m x ^ { 2 } + 3 x - 2 = 0$$

Solve for m

$$m=\frac{x^{3}+3x-2}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 3x from both sides. Anything subtracted from zero gives its negation.

$$x^{3}-mx^{2}-2=-3x$$

Add 2 to both sides.

$$x^{3}-mx^{2}=-3x+2$$

Subtract x^{3} from both sides.

$$-mx^{2}=-3x+2-x^{3}$$

The equation is in standard form.

$$\left(-x^{2}\right)m=2-3x-x^{3}$$

Divide both sides by -x^{2}.

$$\frac{\left(-x^{2}\right)m}{-x^{2}}=\frac{2-3x-x^{3}}{-x^{2}}$$

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

$$m=\frac{2-3x-x^{3}}{-x^{2}}$$

Divide -3x+2-x^{3} by -x^{2}.

$$m=x+\frac{3x-2}{x^{2}}$$