Solve the problem (x+3)^3 + 2(x+3)^2 - 8(x+3) = 0 Do i have to turn into an equation about x?

(x+3)^3 + 2(x+3)^2 - 8(x+3) = 0. To solve the
equation.

We need not turn into an equation in x , as all
the terms are the powers of x+3 and we can treat x+3 itself as one variable t and solve
for t.

So we put  x+3 =
t.

Then the equation changes to t^3+2t^2-8t =
0

We factorise  the
left.

t(t^2+2t-8) =
0....(1).

Consider t^2+2t-8 for further
factorisation:

t^2+2t-8 = t^2+4t-2t -
8

t^2+4t-2t-8 = t(t+4)-2(t+4) =
(t+4)(t-2).

Therefore t^2 +2t-8 =
(t+4)(t-2).

Substituting t^2+2t-8 = (t+4)(t-2) in eq (1),
we get:

t(t+4)(t-2) = 0

Equate
each factor to zero:

t = 0 , t+4 = 0 and t-2 =
0.

t = 0 gives t+3 = 0, x =
-3.

t+4 = 0 gives x+3+4 = 0, x =
-7.

t-2 = 0 gives x+3-2 = 0 , x =
-1.

 Therefore x = -7, x = -3 or x =
-1.