=(2x^3-7x^2+7x)+(2x^3+9x^2-14x)

Solution for =(2x^3-7x^2+7x)+(2x^3+9x^2-14x) equation:

Simplifying
0 = (2x3 + -7x2 + 7x) + (2x3 + 9x2 + -14x)

Reorder the terms:
0 = (7x + -7x2 + 2x3) + (2x3 + 9x2 + -14x)

Remove parenthesis around (7x + -7x2 + 2x3)
0 = 7x + -7x2 + 2x3 + (2x3 + 9x2 + -14x)

Reorder the terms:
0 = 7x + -7x2 + 2x3 + (-14x + 9x2 + 2x3)

Remove parenthesis around (-14x + 9x2 + 2x3)
0 = 7x + -7x2 + 2x3 + -14x + 9x2 + 2x3

Reorder the terms:
0 = 7x + -14x + -7x2 + 9x2 + 2x3 + 2x3

Combine like terms: 7x + -14x = -7x
0 = -7x + -7x2 + 9x2 + 2x3 + 2x3

Combine like terms: -7x2 + 9x2 = 2x2
0 = -7x + 2x2 + 2x3 + 2x3

Combine like terms: 2x3 + 2x3 = 4x3
0 = -7x + 2x2 + 4x3

Solving
0 = -7x + 2x2 + 4x3

Solving for variable 'x'.
Remove the zero:
7x + -2x2 + -4x3 = -7x + 2x2 + 4x3 + 7x + -2x2 + -4x3

Reorder the terms:
7x + -2x2 + -4x3 = -7x + 7x + 2x2 + -2x2 + 4x3 + -4x3

Combine like terms: -7x + 7x = 0
7x + -2x2 + -4x3 = 0 + 2x2 + -2x2 + 4x3 + -4x3
7x + -2x2 + -4x3 = 2x2 + -2x2 + 4x3 + -4x3

Combine like terms: 2x2 + -2x2 = 0
7x + -2x2 + -4x3 = 0 + 4x3 + -4x3
7x + -2x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
7x + -2x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + -2x + -4x2) = 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 '(7 + -2x + -4x2)' equal to zero and attempt to solve:

Simplifying
7 + -2x + -4x2 = 0

Solving
7 + -2x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.75 + 0.5x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 0.5x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 0.5x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 0.5x + x2 = 0 + 1.75
0.5x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
0.5x + x2 = 1.75

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 1.75 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 1.75 + 0.0625

Combine like terms: 1.75 + 0.0625 = 1.8125
0.0625 + 0.5x + x2 = 1.8125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 1.8125

Calculate the square root of the right side: 1.346291202

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.346291202 and -1.346291202.

Subproblem 1
x + 0.25 = 1.346291202

Simplifying
x + 0.25 = 1.346291202

Reorder the terms:
0.25 + x = 1.346291202

Solving
0.25 + x = 1.346291202

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.346291202 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.346291202 + -0.25
x = 1.346291202 + -0.25

Combine like terms: 1.346291202 + -0.25 = 1.096291202
x = 1.096291202

Simplifying
x = 1.096291202

Subproblem 2
x + 0.25 = -1.346291202

Simplifying
x + 0.25 = -1.346291202

Reorder the terms:
0.25 + x = -1.346291202

Solving
0.25 + x = -1.346291202

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.346291202 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.346291202 + -0.25
x = -1.346291202 + -0.25

Combine like terms: -1.346291202 + -0.25 = -1.596291202
x = -1.596291202

Simplifying
x = -1.596291202

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.096291202, -1.596291202}
Solution
x = {0, 1.096291202, -1.596291202}