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

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

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

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

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

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

Combine like terms: -3 + 3 = 0
6 + -8x + 4x2 + -1(0 + 2x2) = 0
6 + -8x + 4x2 + -1(2x2) = 0

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

Multiply -1 * 2
6 + -8x + 4x2 + -2x2 = 0

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

Solving
6 + -8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -4x + x2) = 0

Factor a trinomial.
2((1 + -1x)(3 + -1x)) = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1, 3}