Use the x-intercept method to find all real solutions of the equation. -9x^3-72x^2+36=3x^3+x^2-3x+8

-9x^3-72x^2+36=3x^3+x^2-3x+8                     Add 9x^3 to both sides.

-72x^2 + 36 = 3x^3 + 9x^3 + x^2 - 3x + 8       Add 72x^2 to both sides

36 = 12x^3 +   73x^2 - 3x + 8                           Subtract 36 from both sides.

0 = 12x^3 + 73x^2 - 3x - 28      

It does factor, but it is not very nice.

(x + 6.06)(x - 6.09)(x + 0.632)

If there is any kind of error please report it in a note below.

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.