2(a-2)=3(a+1)

Solution for 2(a-2)=3(a+1) equation:

Simplifying
2(a + -2) = 3(a + 1)

Reorder the terms:
2(-2 + a) = 3(a + 1)
(-2 * 2 + a * 2) = 3(a + 1)
(-4 + 2a) = 3(a + 1)

Reorder the terms:
-4 + 2a = 3(1 + a)
-4 + 2a = (1 * 3 + a * 3)
-4 + 2a = (3 + 3a)

Solving
-4 + 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.
-4 + 2a + -3a = 3 + 3a + -3a

Combine like terms: 2a + -3a = -1a
-4 + -1a = 3 + 3a + -3a

Combine like terms: 3a + -3a = 0
-4 + -1a = 3 + 0
-4 + -1a = 3

Add '4' to each side of the equation.
-4 + 4 + -1a = 3 + 4

Combine like terms: -4 + 4 = 0
0 + -1a = 3 + 4
-1a = 3 + 4

Combine like terms: 3 + 4 = 7
-1a = 7

Divide each side by '-1'.
a = -7

Simplifying
a = -7