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

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

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

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

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

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

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

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

Solving
6 + 1x = -3x + 2x2

Solving for variable 'x'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 2x + -1x2) = 0

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

Ignore the factor 2.
Subproblem 1
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
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}