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

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

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

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

Combine like terms: 2x + 2x = 4x
6 + 4x = x(x + 3)

Reorder the terms:
6 + 4x = x(3 + x)
6 + 4x = (3 * x + x * x)
6 + 4x = (3x + x2)

Solving
6 + 4x = 3x + x2

Solving for variable 'x'.

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

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

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

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

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

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {3, -2}