Solve for x:
8 x^3-12 x^2-2 x = 0
Factor x and constant terms from the left hand side:
2 x (4 x^2-6 x-1) = 0
Divide both sides by 2:
x (4 x^2-6 x-1) = 0
Split into two equations:
x = 0 or 4 x^2-6 x-1 = 0
Divide both sides by 4:
x = 0 or x^2-(3 x)/2-1/4 = 0
Add 1/4 to both sides:
x = 0 or x^2-(3 x)/2 = 1/4
Add 9/16 to both sides:
x = 0 or x^2-(3 x)/2+9/16 = 13/16
Write the left hand side as a square:
x = 0 or (x-3/4)^2 = 13/16
Take the square root of both sides:
x = 0 or x-3/4 = sqrt(13)/4 or x-3/4 = -sqrt(13)/4
Add 3/4 to both sides:
x = 0 or x = 3/4+sqrt(13)/4 or x-3/4 = -sqrt(13)/4
Add 3/4 to both sides:
Answer: | x = 0 or x = 3/4+sqrt(13)/4 or x = 3/4-sqrt(13)/4
