(-6x^2+7x-6)-(8x^2+3x-9)+(7x^2-7x+8)=

Solution for (-6x^2+7x-6)-(8x^2+3x-9)+(7x^2-7x+8)= equation:

Simplifying
(-6x2 + 7x + -6) + -1(8x2 + 3x + -9) + (7x2 + -7x + 8) = 0

Reorder the terms:
(-6 + 7x + -6x2) + -1(8x2 + 3x + -9) + (7x2 + -7x + 8) = 0

Remove parenthesis around (-6 + 7x + -6x2)
-6 + 7x + -6x2 + -1(8x2 + 3x + -9) + (7x2 + -7x + 8) = 0

Reorder the terms:
-6 + 7x + -6x2 + -1(-9 + 3x + 8x2) + (7x2 + -7x + 8) = 0
-6 + 7x + -6x2 + (-9 * -1 + 3x * -1 + 8x2 * -1) + (7x2 + -7x + 8) = 0
-6 + 7x + -6x2 + (9 + -3x + -8x2) + (7x2 + -7x + 8) = 0

Reorder the terms:
-6 + 7x + -6x2 + 9 + -3x + -8x2 + (8 + -7x + 7x2) = 0

Remove parenthesis around (8 + -7x + 7x2)
-6 + 7x + -6x2 + 9 + -3x + -8x2 + 8 + -7x + 7x2 = 0

Reorder the terms:
-6 + 9 + 8 + 7x + -3x + -7x + -6x2 + -8x2 + 7x2 = 0

Combine like terms: -6 + 9 = 3
3 + 8 + 7x + -3x + -7x + -6x2 + -8x2 + 7x2 = 0

Combine like terms: 3 + 8 = 11
11 + 7x + -3x + -7x + -6x2 + -8x2 + 7x2 = 0

Combine like terms: 7x + -3x = 4x
11 + 4x + -7x + -6x2 + -8x2 + 7x2 = 0

Combine like terms: 4x + -7x = -3x
11 + -3x + -6x2 + -8x2 + 7x2 = 0

Combine like terms: -6x2 + -8x2 = -14x2
11 + -3x + -14x2 + 7x2 = 0

Combine like terms: -14x2 + 7x2 = -7x2
11 + -3x + -7x2 = 0

Solving
11 + -3x + -7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-1.571428571 + 0.4285714286x + x2 = 0

Move the constant term to the right:

Add '1.571428571' to each side of the equation.
-1.571428571 + 0.4285714286x + 1.571428571 + x2 = 0 + 1.571428571

Reorder the terms:
-1.571428571 + 1.571428571 + 0.4285714286x + x2 = 0 + 1.571428571

Combine like terms: -1.571428571 + 1.571428571 = 0.000000000
0.000000000 + 0.4285714286x + x2 = 0 + 1.571428571
0.4285714286x + x2 = 0 + 1.571428571

Combine like terms: 0 + 1.571428571 = 1.571428571
0.4285714286x + x2 = 1.571428571

The x term is 0.4285714286x.  Take half its coefficient (0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
0.4285714286x + 0.04591836735 + x2 = 1.571428571 + 0.04591836735

Reorder the terms:
0.04591836735 + 0.4285714286x + x2 = 1.571428571 + 0.04591836735

Combine like terms: 1.571428571 + 0.04591836735 = 1.61734693835
0.04591836735 + 0.4285714286x + x2 = 1.61734693835

Factor a perfect square on the left side:
(x + 0.2142857143)(x + 0.2142857143) = 1.61734693835

Calculate the square root of the right side: 1.271749558

Break this problem into two subproblems by setting 
(x + 0.2142857143) equal to 1.271749558 and -1.271749558.

Subproblem 1
x + 0.2142857143 = 1.271749558

Simplifying
x + 0.2142857143 = 1.271749558

Reorder the terms:
0.2142857143 + x = 1.271749558

Solving
0.2142857143 + x = 1.271749558

Solving for variable 'x'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + x = 1.271749558 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x = 1.271749558 + -0.2142857143
x = 1.271749558 + -0.2142857143

Combine like terms: 1.271749558 + -0.2142857143 = 1.0574638437
x = 1.0574638437

Simplifying
x = 1.0574638437

Subproblem 2
x + 0.2142857143 = -1.271749558

Simplifying
x + 0.2142857143 = -1.271749558

Reorder the terms:
0.2142857143 + x = -1.271749558

Solving
0.2142857143 + x = -1.271749558

Solving for variable 'x'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + x = -1.271749558 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x = -1.271749558 + -0.2142857143
x = -1.271749558 + -0.2142857143

Combine like terms: -1.271749558 + -0.2142857143 = -1.4860352723
x = -1.4860352723

Simplifying
x = -1.4860352723

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0574638437, -1.4860352723}