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

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

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

Multiply (2 + x) * (3 + -1x)
(2(3 + -1x) + x(3 + -1x)) = (6 + -2x)
((3 * 2 + -1x * 2) + x(3 + -1x)) = (6 + -2x)
((6 + -2x) + x(3 + -1x)) = (6 + -2x)
(6 + -2x + (3 * x + -1x * x)) = (6 + -2x)
(6 + -2x + (3x + -1x2)) = (6 + -2x)

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

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

Add '-6' to each side of the equation.
6 + 1x + -6 + -1x2 = 6 + -6 + -2x

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

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

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

Solving
1x + -1x2 = -2x

Solving for variable 'x'.

Reorder the terms:
1x + 2x + -1x2 = -2x + 2x

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + -1x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
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 = {0, 3}