Solve (x+1)^3-x^2(x+3)+2=0

$$( x + 1 ) ^ { 3 } - x ^ { 2 } ( x + 3 ) + 2 = 0$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.

$$x^{3}+3x^{2}+3x+1-x^{2}\left(x+3\right)+2=0$$

Use the distributive property to multiply x^{2} by x+3.

$$x^{3}+3x^{2}+3x+1-\left(x^{3}+3x^{2}\right)+2=0$$

To find the opposite of x^{3}+3x^{2}, find the opposite of each term.

$$x^{3}+3x^{2}+3x+1-x^{3}-3x^{2}+2=0$$

Combine x^{3} and -x^{3} to get 0.

$$3x^{2}+3x+1-3x^{2}+2=0$$

Combine 3x^{2} and -3x^{2} to get 0.

$$3x+1+2=0$$

Add 1 and 2 to get 3.

$$3x+3=0$$

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

$$3x=-3$$

Divide both sides by 3.

$$x=\frac{-3}{3}$$

Divide -3 by 3 to get -1.

$$x=-1$$