(-6x^2+4x-2)-(7x^2-5x-4)+(3x^2-7x+8)=

Solution for (-6x^2+4x-2)-(7x^2-5x-4)+(3x^2-7x+8)= equation:

Simplifying
(-6x2 + 4x + -2) + -1(7x2 + -5x + -4) + (3x2 + -7x + 8) = 0

Reorder the terms:
(-2 + 4x + -6x2) + -1(7x2 + -5x + -4) + (3x2 + -7x + 8) = 0

Remove parenthesis around (-2 + 4x + -6x2)
-2 + 4x + -6x2 + -1(7x2 + -5x + -4) + (3x2 + -7x + 8) = 0

Reorder the terms:
-2 + 4x + -6x2 + -1(-4 + -5x + 7x2) + (3x2 + -7x + 8) = 0
-2 + 4x + -6x2 + (-4 * -1 + -5x * -1 + 7x2 * -1) + (3x2 + -7x + 8) = 0
-2 + 4x + -6x2 + (4 + 5x + -7x2) + (3x2 + -7x + 8) = 0

Reorder the terms:
-2 + 4x + -6x2 + 4 + 5x + -7x2 + (8 + -7x + 3x2) = 0

Remove parenthesis around (8 + -7x + 3x2)
-2 + 4x + -6x2 + 4 + 5x + -7x2 + 8 + -7x + 3x2 = 0

Reorder the terms:
-2 + 4 + 8 + 4x + 5x + -7x + -6x2 + -7x2 + 3x2 = 0

Combine like terms: -2 + 4 = 2
2 + 8 + 4x + 5x + -7x + -6x2 + -7x2 + 3x2 = 0

Combine like terms: 2 + 8 = 10
10 + 4x + 5x + -7x + -6x2 + -7x2 + 3x2 = 0

Combine like terms: 4x + 5x = 9x
10 + 9x + -7x + -6x2 + -7x2 + 3x2 = 0

Combine like terms: 9x + -7x = 2x
10 + 2x + -6x2 + -7x2 + 3x2 = 0

Combine like terms: -6x2 + -7x2 = -13x2
10 + 2x + -13x2 + 3x2 = 0

Combine like terms: -13x2 + 3x2 = -10x2
10 + 2x + -10x2 = 0

Solving
10 + 2x + -10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + x + -5x2)' equal to zero and attempt to solve:

Simplifying
5 + x + -5x2 = 0

Solving
5 + x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1 + -0.2x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.2x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.2x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.2x + x2 = 0 + 1
-0.2x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.2x + x2 = 1

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

Add '0.25' to each side of the equation.
-0.2x + 0.25 + x2 = 1 + 0.25

Reorder the terms:
0.25 + -0.2x + x2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + -0.2x + x2 = 1.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
x + 0.5 = 1.118033989

Simplifying
x + 0.5 = 1.118033989

Reorder the terms:
0.5 + x = 1.118033989

Solving
0.5 + x = 1.118033989

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.118033989 + -0.5
x = 1.118033989 + -0.5

Combine like terms: 1.118033989 + -0.5 = 0.618033989
x = 0.618033989

Simplifying
x = 0.618033989

Subproblem 2
x + 0.5 = -1.118033989

Simplifying
x + 0.5 = -1.118033989

Reorder the terms:
0.5 + x = -1.118033989

Solving
0.5 + x = -1.118033989

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.118033989 + -0.5
x = -1.118033989 + -0.5

Combine like terms: -1.118033989 + -0.5 = -1.618033989
x = -1.618033989

Simplifying
x = -1.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.618033989, -1.618033989}
Solution
x = {0.618033989, -1.618033989}