14x^3+(3*-3)6x^2-10x=-x

Solution for 14x^3+(3*-3)6x^2-10x=-x equation:

Simplifying
14x3 + (3 * -3) * 6x2 + -10x = -1x

Multiply 3 * -3
14x3 + (-9) * 6x2 + -10x = -1x

Multiply -9 * 6
14x3 + -54x2 + -10x = -1x

Reorder the terms:
-10x + -54x2 + 14x3 = -1x

Solving
-10x + -54x2 + 14x3 = -1x

Solving for variable 'x'.

Reorder the terms:
-10x + x + -54x2 + 14x3 = -1x + x

Combine like terms: -10x + x = -9x
-9x + -54x2 + 14x3 = -1x + x

Combine like terms: -1x + x = 0
-9x + -54x2 + 14x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-9 + -54x + 14x2) = 0

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 '(-9 + -54x + 14x2)' equal to zero and attempt to solve:

Simplifying
-9 + -54x + 14x2 = 0

Solving
-9 + -54x + 14x2 = 0

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

Divide each side by '14'.
-0.6428571429 + -3.857142857x + x2 = 0

Move the constant term to the right:

Add '0.6428571429' to each side of the equation.
-0.6428571429 + -3.857142857x + 0.6428571429 + x2 = 0 + 0.6428571429

Reorder the terms:
-0.6428571429 + 0.6428571429 + -3.857142857x + x2 = 0 + 0.6428571429

Combine like terms: -0.6428571429 + 0.6428571429 = 0.0000000000
0.0000000000 + -3.857142857x + x2 = 0 + 0.6428571429
-3.857142857x + x2 = 0 + 0.6428571429

Combine like terms: 0 + 0.6428571429 = 0.6428571429
-3.857142857x + x2 = 0.6428571429

The x term is -3.857142857x.  Take half its coefficient (-1.928571429).
Square it (3.719387757) and add it to both sides.

Add '3.719387757' to each side of the equation.
-3.857142857x + 3.719387757 + x2 = 0.6428571429 + 3.719387757

Reorder the terms:
3.719387757 + -3.857142857x + x2 = 0.6428571429 + 3.719387757

Combine like terms: 0.6428571429 + 3.719387757 = 4.3622448999
3.719387757 + -3.857142857x + x2 = 4.3622448999

Factor a perfect square on the left side:
(x + -1.928571429)(x + -1.928571429) = 4.3622448999

Calculate the square root of the right side: 2.088598789

Break this problem into two subproblems by setting 
(x + -1.928571429) equal to 2.088598789 and -2.088598789.

Subproblem 1
x + -1.928571429 = 2.088598789

Simplifying
x + -1.928571429 = 2.088598789

Reorder the terms:
-1.928571429 + x = 2.088598789

Solving
-1.928571429 + x = 2.088598789

Solving for variable 'x'.

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

Add '1.928571429' to each side of the equation.
-1.928571429 + 1.928571429 + x = 2.088598789 + 1.928571429

Combine like terms: -1.928571429 + 1.928571429 = 0.000000000
0.000000000 + x = 2.088598789 + 1.928571429
x = 2.088598789 + 1.928571429

Combine like terms: 2.088598789 + 1.928571429 = 4.017170218
x = 4.017170218

Simplifying
x = 4.017170218

Subproblem 2
x + -1.928571429 = -2.088598789

Simplifying
x + -1.928571429 = -2.088598789

Reorder the terms:
-1.928571429 + x = -2.088598789

Solving
-1.928571429 + x = -2.088598789

Solving for variable 'x'.

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

Add '1.928571429' to each side of the equation.
-1.928571429 + 1.928571429 + x = -2.088598789 + 1.928571429

Combine like terms: -1.928571429 + 1.928571429 = 0.000000000
0.000000000 + x = -2.088598789 + 1.928571429
x = -2.088598789 + 1.928571429

Combine like terms: -2.088598789 + 1.928571429 = -0.16002736
x = -0.16002736

Simplifying
x = -0.16002736

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.017170218, -0.16002736}
Solution
x = {0, 4.017170218, -0.16002736}