Solve the following quadratic equation: x(x^2 - 1)(x+2) + 1 = 0

The key is to follow the proper
order.

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

First multiply the x on the left times everything in
the first parantheses.

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

Next multiply the two parentheses. You have to
multiply the first number in the first parentheses (x^3) by everything in the second
parentheses, then multiply the second number in the first parentheses by everything in
the second parentheses.

(x^4+2x-x^2-2x)
+1=0

Simplify the parentheses by adding and
subtracting like terms (x^4 - x^2) and (2x-2x)

(x^2)
+1=0

Now get the variable alone on one side of the equal
sign.

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

(x^2)
=-1

To simplify to x we must find the square root. The
square root of (x^2) is x. What we do to one side we must do to the other, so we also
have to find the square root of -1. Square roots of negative numbers do not exist
so

x= 1i