(13x^3+9x^4-13x^2)-(-14x^2+10x^2+14x^3)=

Solution for (13x^3+9x^4-13x^2)-(-14x^2+10x^2+14x^3)= equation:

Simplifying
(13x3 + 9x4 + -13x2) + -1(-14x2 + 10x2 + 14x3) = 0

Reorder the terms:
(-13x2 + 13x3 + 9x4) + -1(-14x2 + 10x2 + 14x3) = 0

Remove parenthesis around (-13x2 + 13x3 + 9x4)
-13x2 + 13x3 + 9x4 + -1(-14x2 + 10x2 + 14x3) = 0

Combine like terms: -14x2 + 10x2 = -4x2
-13x2 + 13x3 + 9x4 + -1(-4x2 + 14x3) = 0
-13x2 + 13x3 + 9x4 + (-4x2 * -1 + 14x3 * -1) = 0
-13x2 + 13x3 + 9x4 + (4x2 + -14x3) = 0

Reorder the terms:
-13x2 + 4x2 + 13x3 + -14x3 + 9x4 = 0

Combine like terms: -13x2 + 4x2 = -9x2
-9x2 + 13x3 + -14x3 + 9x4 = 0

Combine like terms: 13x3 + -14x3 = -1x3
-9x2 + -1x3 + 9x4 = 0

Solving
-9x2 + -1x3 + 9x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-9 + -1x + 9x2) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(-9 + -1x + 9x2)' equal to zero and attempt to solve:

Simplifying
-9 + -1x + 9x2 = 0

Solving
-9 + -1x + 9x2 = 0

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

Divide each side by '9'.
-1 + -0.1111111111x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.1111111111x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.1111111111x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.1111111111x + x2 = 0 + 1
-0.1111111111x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.1111111111x + x2 = 1

The x term is -0.1111111111x.  Take half its coefficient (-0.05555555555).
Square it (0.003086419752) and add it to both sides.

Add '0.003086419752' to each side of the equation.
-0.1111111111x + 0.003086419752 + x2 = 1 + 0.003086419752

Reorder the terms:
0.003086419752 + -0.1111111111x + x2 = 1 + 0.003086419752

Combine like terms: 1 + 0.003086419752 = 1.003086419752
0.003086419752 + -0.1111111111x + x2 = 1.003086419752

Factor a perfect square on the left side:
(x + -0.05555555555)(x + -0.05555555555) = 1.003086419752

Calculate the square root of the right side: 1.001542021

Break this problem into two subproblems by setting 
(x + -0.05555555555) equal to 1.001542021 and -1.001542021.

Subproblem 1
x + -0.05555555555 = 1.001542021

Simplifying
x + -0.05555555555 = 1.001542021

Reorder the terms:
-0.05555555555 + x = 1.001542021

Solving
-0.05555555555 + x = 1.001542021

Solving for variable 'x'.

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

Add '0.05555555555' to each side of the equation.
-0.05555555555 + 0.05555555555 + x = 1.001542021 + 0.05555555555

Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000
0.00000000000 + x = 1.001542021 + 0.05555555555
x = 1.001542021 + 0.05555555555

Combine like terms: 1.001542021 + 0.05555555555 = 1.05709757655
x = 1.05709757655

Simplifying
x = 1.05709757655

Subproblem 2
x + -0.05555555555 = -1.001542021

Simplifying
x + -0.05555555555 = -1.001542021

Reorder the terms:
-0.05555555555 + x = -1.001542021

Solving
-0.05555555555 + x = -1.001542021

Solving for variable 'x'.

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

Add '0.05555555555' to each side of the equation.
-0.05555555555 + 0.05555555555 + x = -1.001542021 + 0.05555555555

Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000
0.00000000000 + x = -1.001542021 + 0.05555555555
x = -1.001542021 + 0.05555555555

Combine like terms: -1.001542021 + 0.05555555555 = -0.94598646545
x = -0.94598646545

Simplifying
x = -0.94598646545

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.05709757655, -0.94598646545}
Solution
x = {0, 1.05709757655, -0.94598646545}