2(2a+3)+3(a+1)=30

Solution for 2(2a+3)+3(a+1)=30 equation:

Simplifying
2(2a + 3) + 3(a + 1) = 30

Reorder the terms:
2(3 + 2a) + 3(a + 1) = 30
(3 * 2 + 2a * 2) + 3(a + 1) = 30
(6 + 4a) + 3(a + 1) = 30

Reorder the terms:
6 + 4a + 3(1 + a) = 30
6 + 4a + (1 * 3 + a * 3) = 30
6 + 4a + (3 + 3a) = 30

Reorder the terms:
6 + 3 + 4a + 3a = 30

Combine like terms: 6 + 3 = 9
9 + 4a + 3a = 30

Combine like terms: 4a + 3a = 7a
9 + 7a = 30

Solving
9 + 7a = 30

Solving for variable 'a'.

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

Add '-9' to each side of the equation.
9 + -9 + 7a = 30 + -9

Combine like terms: 9 + -9 = 0
0 + 7a = 30 + -9
7a = 30 + -9

Combine like terms: 30 + -9 = 21
7a = 21

Divide each side by '7'.
a = 3

Simplifying
a = 3