What has been given is not an equation but the product of two terms

(x+9)(x^3+3x-8)

=> x^4 + 9x^3 + 3x^2 + 27x - 8x - 72

If the equation to be solved is (x+9)(x^3+3x-8) = 0, equate each of the terms to 0.

x + 9 = 0

=> x = -9

x^3+3x-8 = 0 can be solved by factorization. The function provided in the link to find roots of a cubic equation has to be used. This gives the roots: `(sqrt(17)+4)^(1/3)*(-sqrt(3)*i/2-1/2)-(sqrt(3)*i/2-1/2)/(sqrt(17)+4)^(1/3)`, `(sqrt(17)+4)^(1/3)*(sqrt(3)*i/2-1/2)-(-sqrt(3)*i/2-1/2)/(sqrt(17)+4)^(1/3)` and `(sqrt(17)+4)^(1/3)-1/(sqrt(17)+4)^(1/3) `

multiply each term in the first bracket by each term in the second

(x^4+3x^2-8x+9x3+27x-72)

collect like terms

(x^4+9x^3+3x^2+27x-8x-72)

(x^4+9x^3+3x^2+19x-72)

You can use Pascal's Triangle to solve this.