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

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

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

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

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

Solving
2 + 2a = -6 + 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 = -6 + 3a + -3a

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

Combine like terms: 3a + -3a = 0
2 + -1a = -6 + 0
2 + -1a = -6

Add '-2' to each side of the equation.
2 + -2 + -1a = -6 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = -6 + -2
-1a = -6 + -2

Combine like terms: -6 + -2 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8