### Home > PC > Chapter 8 > Lesson 8.2.1 > Problem 8-76

8-76.

Solve *x*^{3}(*x* + 3)^{4} + 2*x*^{2}(*x* + 3)^{3} = 0. Hint: Let *a* = *x* + 3 and factor. Homework Help ✎

Substitute *a* for *x* + 3:

Factor:

Set each factor = 0:

Substitute (*x* + 3) back in the expressions and solve.

*x*^{3}*a*^{4} + 2*x*^{2}*a*^{3} = 0

*x*^{2}*a*^{3}(*ax* + 2) = 0

*x*^{2}*a*^{3} = 0 or *ax* + 2 = 0

*x*^{2}(*x* + 3)^{3} = 0*x*^{2} = 0*x* = 0

(*x* + 3)^{3} = 0*x* = −3

*ax* + 2 = 0

(*x* + 3)*x* + 2 = 0*x*^{2} + 3*x* + 2 = 0

(*x* + 2)(*x* + 1) = 0*x* = −2; *x* = −1