x^3 - 7x = 6x -12
Subtract 6x from both sides:
x^3 - 13x = -12
Add 12 to both sides:
x^3 - 13x +12 = 0
Factor the left side:
(x-3) (x-1)(x+4) = 0
Now solve for x in each set of parenthesis so they all equal 0:
x = 3
x = 1
x = -4
The roots are 3,1, -4