(4x^2+5x-6)+(4x^2-4x-2)-(-x^2-9x+1)=

Solution for (4x^2+5x-6)+(4x^2-4x-2)-(-x^2-9x+1)= equation:

Simplifying
(4x2 + 5x + -6) + (4x2 + -4x + -2) + -1(-1x2 + -9x + 1) = 0

Reorder the terms:
(-6 + 5x + 4x2) + (4x2 + -4x + -2) + -1(-1x2 + -9x + 1) = 0

Remove parenthesis around (-6 + 5x + 4x2)
-6 + 5x + 4x2 + (4x2 + -4x + -2) + -1(-1x2 + -9x + 1) = 0

Reorder the terms:
-6 + 5x + 4x2 + (-2 + -4x + 4x2) + -1(-1x2 + -9x + 1) = 0

Remove parenthesis around (-2 + -4x + 4x2)
-6 + 5x + 4x2 + -2 + -4x + 4x2 + -1(-1x2 + -9x + 1) = 0

Reorder the terms:
-6 + 5x + 4x2 + -2 + -4x + 4x2 + -1(1 + -9x + -1x2) = 0
-6 + 5x + 4x2 + -2 + -4x + 4x2 + (1 * -1 + -9x * -1 + -1x2 * -1) = 0
-6 + 5x + 4x2 + -2 + -4x + 4x2 + (-1 + 9x + 1x2) = 0

Reorder the terms:
-6 + -2 + -1 + 5x + -4x + 9x + 4x2 + 4x2 + 1x2 = 0

Combine like terms: -6 + -2 = -8
-8 + -1 + 5x + -4x + 9x + 4x2 + 4x2 + 1x2 = 0

Combine like terms: -8 + -1 = -9
-9 + 5x + -4x + 9x + 4x2 + 4x2 + 1x2 = 0

Combine like terms: 5x + -4x = 1x
-9 + 1x + 9x + 4x2 + 4x2 + 1x2 = 0

Combine like terms: 1x + 9x = 10x
-9 + 10x + 4x2 + 4x2 + 1x2 = 0

Combine like terms: 4x2 + 4x2 = 8x2
-9 + 10x + 8x2 + 1x2 = 0

Combine like terms: 8x2 + 1x2 = 9x2
-9 + 10x + 9x2 = 0

Solving
-9 + 10x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-1 + 1.111111111x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.111111111x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.111111111x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.111111111x + x2 = 0 + 1
1.111111111x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.111111111x + x2 = 1

The x term is 1.111111111x.  Take half its coefficient (0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
1.111111111x + 0.3086419752 + x2 = 1 + 0.3086419752

Reorder the terms:
0.3086419752 + 1.111111111x + x2 = 1 + 0.3086419752

Combine like terms: 1 + 0.3086419752 = 1.3086419752
0.3086419752 + 1.111111111x + x2 = 1.3086419752

Factor a perfect square on the left side:
(x + 0.5555555555)(x + 0.5555555555) = 1.3086419752

Calculate the square root of the right side: 1.143958905

Break this problem into two subproblems by setting 
(x + 0.5555555555) equal to 1.143958905 and -1.143958905.

Subproblem 1
x + 0.5555555555 = 1.143958905

Simplifying
x + 0.5555555555 = 1.143958905

Reorder the terms:
0.5555555555 + x = 1.143958905

Solving
0.5555555555 + x = 1.143958905

Solving for variable 'x'.

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

Add '-0.5555555555' to each side of the equation.
0.5555555555 + -0.5555555555 + x = 1.143958905 + -0.5555555555

Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000
0.0000000000 + x = 1.143958905 + -0.5555555555
x = 1.143958905 + -0.5555555555

Combine like terms: 1.143958905 + -0.5555555555 = 0.5884033495
x = 0.5884033495

Simplifying
x = 0.5884033495

Subproblem 2
x + 0.5555555555 = -1.143958905

Simplifying
x + 0.5555555555 = -1.143958905

Reorder the terms:
0.5555555555 + x = -1.143958905

Solving
0.5555555555 + x = -1.143958905

Solving for variable 'x'.

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

Add '-0.5555555555' to each side of the equation.
0.5555555555 + -0.5555555555 + x = -1.143958905 + -0.5555555555

Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000
0.0000000000 + x = -1.143958905 + -0.5555555555
x = -1.143958905 + -0.5555555555

Combine like terms: -1.143958905 + -0.5555555555 = -1.6995144605
x = -1.6995144605

Simplifying
x = -1.6995144605

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5884033495, -1.6995144605}