Polynomial algebra

Question

How do you solve this equation and how to get the answer?

Answer 1

= 0

This equation is amenable to factor by grouping:

x (x^2 + 4) + 7 (x^2 + 4) = 0

Seeing the common factor of the two terms is x^2 + 4, we can further factor:

(x^2 + 4)(x + 7) = 0

which means either x^2 + 4 = 0 --> x^2 = -4 --> x = +/- sqrt(-4) --> x = +/- i*sqrt(4) --> x = +/- 2i

or x + 7 = 0 --> x = -7

Answer 2

Factor it: x(x² + 4) + 7(x² + 4) = (x+7)(x² + 4)

Set each factor = 0

Roots are -7, 2i and -2i