2(2a+1)=3(a+4)

Solution for 2(2a+1)=3(a+4) equation:

Simplifying
2(2a + 1) = 3(a + 4)

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

Reorder the terms:
2 + 4a = 3(4 + a)
2 + 4a = (4 * 3 + a * 3)
2 + 4a = (12 + 3a)

Solving
2 + 4a = 12 + 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 + 4a + -3a = 12 + 3a + -3a

Combine like terms: 4a + -3a = 1a
2 + 1a = 12 + 3a + -3a

Combine like terms: 3a + -3a = 0
2 + 1a = 12 + 0
2 + 1a = 12

Add '-2' to each side of the equation.
2 + -2 + 1a = 12 + -2

Combine like terms: 2 + -2 = 0
0 + 1a = 12 + -2
1a = 12 + -2

Combine like terms: 12 + -2 = 10
1a = 10

Divide each side by '1'.
a = 10

Simplifying
a = 10