2(a+3)=5(a-1)-7(a-3)

Solution for 2(a+3)=5(a-1)-7(a-3) equation:

Simplifying
2(a + 3) = 5(a + -1) + -7(a + -3)

Reorder the terms:
2(3 + a) = 5(a + -1) + -7(a + -3)
(3 * 2 + a * 2) = 5(a + -1) + -7(a + -3)
(6 + 2a) = 5(a + -1) + -7(a + -3)

Reorder the terms:
6 + 2a = 5(-1 + a) + -7(a + -3)
6 + 2a = (-1 * 5 + a * 5) + -7(a + -3)
6 + 2a = (-5 + 5a) + -7(a + -3)

Reorder the terms:
6 + 2a = -5 + 5a + -7(-3 + a)
6 + 2a = -5 + 5a + (-3 * -7 + a * -7)
6 + 2a = -5 + 5a + (21 + -7a)

Reorder the terms:
6 + 2a = -5 + 21 + 5a + -7a

Combine like terms: -5 + 21 = 16
6 + 2a = 16 + 5a + -7a

Combine like terms: 5a + -7a = -2a
6 + 2a = 16 + -2a

Solving
6 + 2a = 16 + -2a

Solving for variable 'a'.

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

Add '2a' to each side of the equation.
6 + 2a + 2a = 16 + -2a + 2a

Combine like terms: 2a + 2a = 4a
6 + 4a = 16 + -2a + 2a

Combine like terms: -2a + 2a = 0
6 + 4a = 16 + 0
6 + 4a = 16

Add '-6' to each side of the equation.
6 + -6 + 4a = 16 + -6

Combine like terms: 6 + -6 = 0
0 + 4a = 16 + -6
4a = 16 + -6

Combine like terms: 16 + -6 = 10
4a = 10

Divide each side by '4'.
a = 2.5

Simplifying
a = 2.5