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

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

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

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

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

Solving
6 + 2x = -6 + 3x

Solving for variable 'x'.

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

Add '-3x' to each side of the equation.
6 + 2x + -3x = -6 + 3x + -3x

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

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

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

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

Combine like terms: -6 + -6 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12