Solve θx^3+θx^2+θx=0!

$$\theta { x }^{ 3 } + \theta { x }^{ 2 } + \theta x=0 !$$

Solve for θ

$$\theta =\frac{1}{x\left(x^{2}+x+1\right)}$$

$$x\neq 0$$

Steps for Solving Linear Equation

The factorial of 0 is 1.

$$\theta x^{3}+\theta x^{2}+\theta x=1$$

Combine all terms containing \theta .

$$\left(x^{3}+x^{2}+x\right)\theta =1$$

Divide both sides by x^{3}+x^{2}+x.

$$\frac{\left(x^{3}+x^{2}+x\right)\theta }{x^{3}+x^{2}+x}=\frac{1}{x^{3}+x^{2}+x}$$

Dividing by x^{3}+x^{2}+x undoes the multiplication by x^{3}+x^{2}+x.

$$\theta =\frac{1}{x^{3}+x^{2}+x}$$

Divide 1 by x^{3}+x^{2}+x.

$$\theta =\frac{1}{x\left(x^{2}+x+1\right)}$$

Solve for x

$$x=\frac{2^{\frac{2}{3}}\left(\sqrt[3]{3\theta \sqrt{3\left(3\theta ^{2}+14\theta +27\right)}+7\theta |\theta |+27|\theta |}+\sqrt[3]{-3\theta \sqrt{3\left(3\theta ^{2}+14\theta +27\right)}+7\theta |\theta |+27|\theta |}-\sqrt[3]{2\theta |\theta |}\right)}{6\sqrt[3]{\theta |\theta |}}$$