5(2a+3)-2(a-4)=3(2a+2)+a

Solution for 5(2a+3)-2(a-4)=3(2a+2)+a equation:

Simplifying
5(2a + 3) + -2(a + -4) = 3(2a + 2) + a

Reorder the terms:
5(3 + 2a) + -2(a + -4) = 3(2a + 2) + a
(3 * 5 + 2a * 5) + -2(a + -4) = 3(2a + 2) + a
(15 + 10a) + -2(a + -4) = 3(2a + 2) + a

Reorder the terms:
15 + 10a + -2(-4 + a) = 3(2a + 2) + a
15 + 10a + (-4 * -2 + a * -2) = 3(2a + 2) + a
15 + 10a + (8 + -2a) = 3(2a + 2) + a

Reorder the terms:
15 + 8 + 10a + -2a = 3(2a + 2) + a

Combine like terms: 15 + 8 = 23
23 + 10a + -2a = 3(2a + 2) + a

Combine like terms: 10a + -2a = 8a
23 + 8a = 3(2a + 2) + a

Reorder the terms:
23 + 8a = 3(2 + 2a) + a
23 + 8a = (2 * 3 + 2a * 3) + a
23 + 8a = (6 + 6a) + a

Combine like terms: 6a + a = 7a
23 + 8a = 6 + 7a

Solving
23 + 8a = 6 + 7a

Solving for variable 'a'.

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

Add '-7a' to each side of the equation.
23 + 8a + -7a = 6 + 7a + -7a

Combine like terms: 8a + -7a = 1a
23 + 1a = 6 + 7a + -7a

Combine like terms: 7a + -7a = 0
23 + 1a = 6 + 0
23 + 1a = 6

Add '-23' to each side of the equation.
23 + -23 + 1a = 6 + -23

Combine like terms: 23 + -23 = 0
0 + 1a = 6 + -23
1a = 6 + -23

Combine like terms: 6 + -23 = -17
1a = -17

Divide each side by '1'.
a = -17

Simplifying
a = -17