Solve for x:
5 x^4-2 x^3+3 x^2 = 0
Factor x^2 from the left hand side:
x^2 (5 x^2-2 x+3) = 0
Split into two equations:
x^2 = 0 or 5 x^2-2 x+3 = 0
Take the square root of both sides:
x = 0 or 5 x^2-2 x+3 = 0
Divide both sides by 5:
x = 0 or x^2-(2 x)/5+3/5 = 0
Subtract 3/5 from both sides:
x = 0 or x^2-(2 x)/5 = -3/5
Add 1/25 to both sides:
x = 0 or x^2-(2 x)/5+1/25 = -14/25
Write the left hand side as a square:
x = 0 or (x-1/5)^2 = -14/25
Take the square root of both sides:
x = 0 or x-1/5 = (i sqrt(14))/5 or x-1/5 = 1/5 (-i) sqrt(14)
Add 1/5 to both sides:
x = 0 or x = 1/5+(i sqrt(14))/5 or x-1/5 = -(i sqrt(14))/5
Add 1/5 to both sides:
Answer: |x = 0 or x = 1/5+(i sqrt(14))/5 or x = 1/5-(i sqrt(14))/5
