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

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

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

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

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

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

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

Combine like terms: 2x + -3x = -1x
-2 + -1x + 1x2 = 0

Solving
-2 + -1x + 1x2 = 0

Solving for variable 'x'.

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

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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 2}