4x^3-4x^2+84x=0

Solution for 4x^3-4x^2+84x=0 equation:

Simplifying
4x3 + -4x2 + 84x = 0

Reorder the terms:
84x + -4x2 + 4x3 = 0

Solving
84x + -4x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(21 + -1x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(21 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
21 + -1x + x2 = 0

Solving
21 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -1x + -21 + x2 = 0 + -21

Reorder the terms:
21 + -21 + -1x + x2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x + x2 = 0 + -21
-1x + x2 = 0 + -21

Combine like terms: 0 + -21 = -21
-1x + x2 = -21

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -21 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -21 + 0.25

Combine like terms: -21 + 0.25 = -20.75
0.25 + -1x + x2 = -20.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -20.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}