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

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

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

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

Reorder the terms:
6 + 2x = 3x(3 + x)
6 + 2x = (3 * 3x + x * 3x)
6 + 2x = (9x + 3x2)

Solving
6 + 2x = 9x + 3x2

Solving for variable 'x'.

Combine like terms: 2x + -9x = -7x
6 + -7x + -3x2 = 9x + 3x2 + -9x + -3x2

Reorder the terms:
6 + -7x + -3x2 = 9x + -9x + 3x2 + -3x2

Combine like terms: 9x + -9x = 0
6 + -7x + -3x2 = 0 + 3x2 + -3x2
6 + -7x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
6 + -7x + -3x2 = 0

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

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Subproblem 2
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
Solution
x = {0.6666666667, -3}