Question

How do I solve this x^2(x+1)-x(x+1)-6(x-1)=0 no idea how to make -6(x-1) to be 6(x+1) and factor out it. Be able to follow the comment

Answer 1

X²(X+1) - X(X+1) - 6(X-1) = 0

=> X³ - X - 6X + 6 = 0

=> X³ - 7X + 6 = 0

Now, we can use vanishing method to solve this.

We can notice that if we put X = 1, then the equation satisfy.

So, we can proceed like,

X²(X - 1) + X(X - 1) + -6(X - 1) = 0

=> (X - 1)(X² + X - 6) = 0

=> (X - 1)(X² +3X - 2X - 6) = 0

=> (X - 1){X(X +3) - 2*(X + 3)} = 0

=> (X - 1)(X + 3)(X - 2) = 0

So, the values of X is -3,1 and 2.