0=-18x^3+94x^2-84x

Solution for 0=-18x^3+94x^2-84x equation:

Simplifying
0 = -18x3 + 94x2 + -84x

Reorder the terms:
0 = -84x + 94x2 + -18x3

Solving
0 = -84x + 94x2 + -18x3

Solving for variable 'x'.
Remove the zero:
84x + -94x2 + 18x3 = -84x + 94x2 + -18x3 + 84x + -94x2 + 18x3

Reorder the terms:
84x + -94x2 + 18x3 = -84x + 84x + 94x2 + -94x2 + -18x3 + 18x3

Combine like terms: -84x + 84x = 0
84x + -94x2 + 18x3 = 0 + 94x2 + -94x2 + -18x3 + 18x3
84x + -94x2 + 18x3 = 94x2 + -94x2 + -18x3 + 18x3

Combine like terms: 94x2 + -94x2 = 0
84x + -94x2 + 18x3 = 0 + -18x3 + 18x3
84x + -94x2 + 18x3 = -18x3 + 18x3

Combine like terms: -18x3 + 18x3 = 0
84x + -94x2 + 18x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(42 + -47x + 9x2) = 0

Ignore the factor 2.
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 '(42 + -47x + 9x2)' equal to zero and attempt to solve:

Simplifying
42 + -47x + 9x2 = 0

Solving
42 + -47x + 9x2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
4.666666667 + -5.222222222x + x2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + -5.222222222x + -4.666666667 + x2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + -5.222222222x + x2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + -5.222222222x + x2 = 0 + -4.666666667
-5.222222222x + x2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
-5.222222222x + x2 = -4.666666667

The x term is -5.222222222x.  Take half its coefficient (-2.611111111).
Square it (6.817901234) and add it to both sides.

Add '6.817901234' to each side of the equation.
-5.222222222x + 6.817901234 + x2 = -4.666666667 + 6.817901234

Reorder the terms:
6.817901234 + -5.222222222x + x2 = -4.666666667 + 6.817901234

Combine like terms: -4.666666667 + 6.817901234 = 2.151234567
6.817901234 + -5.222222222x + x2 = 2.151234567

Factor a perfect square on the left side:
(x + -2.611111111)(x + -2.611111111) = 2.151234567

Calculate the square root of the right side: 1.466708753

Break this problem into two subproblems by setting 
(x + -2.611111111) equal to 1.466708753 and -1.466708753.

Subproblem 1
x + -2.611111111 = 1.466708753

Simplifying
x + -2.611111111 = 1.466708753

Reorder the terms:
-2.611111111 + x = 1.466708753

Solving
-2.611111111 + x = 1.466708753

Solving for variable 'x'.

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

Add '2.611111111' to each side of the equation.
-2.611111111 + 2.611111111 + x = 1.466708753 + 2.611111111

Combine like terms: -2.611111111 + 2.611111111 = 0.000000000
0.000000000 + x = 1.466708753 + 2.611111111
x = 1.466708753 + 2.611111111

Combine like terms: 1.466708753 + 2.611111111 = 4.077819864
x = 4.077819864

Simplifying
x = 4.077819864

Subproblem 2
x + -2.611111111 = -1.466708753

Simplifying
x + -2.611111111 = -1.466708753

Reorder the terms:
-2.611111111 + x = -1.466708753

Solving
-2.611111111 + x = -1.466708753

Solving for variable 'x'.

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

Add '2.611111111' to each side of the equation.
-2.611111111 + 2.611111111 + x = -1.466708753 + 2.611111111

Combine like terms: -2.611111111 + 2.611111111 = 0.000000000
0.000000000 + x = -1.466708753 + 2.611111111
x = -1.466708753 + 2.611111111

Combine like terms: -1.466708753 + 2.611111111 = 1.144402358
x = 1.144402358

Simplifying
x = 1.144402358

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.077819864, 1.144402358}
Solution
x = {0, 4.077819864, 1.144402358}