2[a-1]=3[a+1]

Solution for 2[a-1]=3[a+1] equation:

Simplifying
2[a + -1] = 3[a + 1]

Reorder the terms:
2[-1 + a] = 3[a + 1]
[-1 * 2 + a * 2] = 3[a + 1]
[-2 + 2a] = 3[a + 1]

Reorder the terms:
-2 + 2a = 3[1 + a]
-2 + 2a = [1 * 3 + a * 3]
-2 + 2a = [3 + 3a]

Solving
-2 + 2a = 3 + 3a

Solving for variable 'a'.

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

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

Combine like terms: 2a + -3a = -1a
-2 + -1a = 3 + 3a + -3a

Combine like terms: 3a + -3a = 0
-2 + -1a = 3 + 0
-2 + -1a = 3

Add '2' to each side of the equation.
-2 + 2 + -1a = 3 + 2

Combine like terms: -2 + 2 = 0
0 + -1a = 3 + 2
-1a = 3 + 2

Combine like terms: 3 + 2 = 5
-1a = 5

Divide each side by '-1'.
a = -5

Simplifying
a = -5