3(a+1)+2(2a-3)=5(a-1)+8

Solution for 3(a+1)+2(2a-3)=5(a-1)+8 equation:

Simplifying
3(a + 1) + 2(2a + -3) = 5(a + -1) + 8

Reorder the terms:
3(1 + a) + 2(2a + -3) = 5(a + -1) + 8
(1 * 3 + a * 3) + 2(2a + -3) = 5(a + -1) + 8
(3 + 3a) + 2(2a + -3) = 5(a + -1) + 8

Reorder the terms:
3 + 3a + 2(-3 + 2a) = 5(a + -1) + 8
3 + 3a + (-3 * 2 + 2a * 2) = 5(a + -1) + 8
3 + 3a + (-6 + 4a) = 5(a + -1) + 8

Reorder the terms:
3 + -6 + 3a + 4a = 5(a + -1) + 8

Combine like terms: 3 + -6 = -3
-3 + 3a + 4a = 5(a + -1) + 8

Combine like terms: 3a + 4a = 7a
-3 + 7a = 5(a + -1) + 8

Reorder the terms:
-3 + 7a = 5(-1 + a) + 8
-3 + 7a = (-1 * 5 + a * 5) + 8
-3 + 7a = (-5 + 5a) + 8

Reorder the terms:
-3 + 7a = -5 + 8 + 5a

Combine like terms: -5 + 8 = 3
-3 + 7a = 3 + 5a

Solving
-3 + 7a = 3 + 5a

Solving for variable 'a'.

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

Add '-5a' to each side of the equation.
-3 + 7a + -5a = 3 + 5a + -5a

Combine like terms: 7a + -5a = 2a
-3 + 2a = 3 + 5a + -5a

Combine like terms: 5a + -5a = 0
-3 + 2a = 3 + 0
-3 + 2a = 3

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

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

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

Divide each side by '2'.
a = 3

Simplifying
a = 3