3x(x+2)-x(x-2)+6=0

Solution for 3x(x+2)-x(x-2)+6=0 equation:

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

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

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

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

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

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

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