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

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

Simplifying
(2a + 1)(a + 3) + -1(2a + 1)(a + -3) = 0

Reorder the terms:
(1 + 2a)(a + 3) + -1(2a + 1)(a + -3) = 0

Reorder the terms:
(1 + 2a)(3 + a) + -1(2a + 1)(a + -3) = 0

Multiply (1 + 2a) * (3 + a)
(1(3 + a) + 2a * (3 + a)) + -1(2a + 1)(a + -3) = 0
((3 * 1 + a * 1) + 2a * (3 + a)) + -1(2a + 1)(a + -3) = 0
((3 + 1a) + 2a * (3 + a)) + -1(2a + 1)(a + -3) = 0
(3 + 1a + (3 * 2a + a * 2a)) + -1(2a + 1)(a + -3) = 0
(3 + 1a + (6a + 2a2)) + -1(2a + 1)(a + -3) = 0

Combine like terms: 1a + 6a = 7a
(3 + 7a + 2a2) + -1(2a + 1)(a + -3) = 0

Reorder the terms:
3 + 7a + 2a2 + -1(1 + 2a)(a + -3) = 0

Reorder the terms:
3 + 7a + 2a2 + -1(1 + 2a)(-3 + a) = 0

Multiply (1 + 2a) * (-3 + a)
3 + 7a + 2a2 + -1(1(-3 + a) + 2a * (-3 + a)) = 0
3 + 7a + 2a2 + -1((-3 * 1 + a * 1) + 2a * (-3 + a)) = 0
3 + 7a + 2a2 + -1((-3 + 1a) + 2a * (-3 + a)) = 0
3 + 7a + 2a2 + -1(-3 + 1a + (-3 * 2a + a * 2a)) = 0
3 + 7a + 2a2 + -1(-3 + 1a + (-6a + 2a2)) = 0

Combine like terms: 1a + -6a = -5a
3 + 7a + 2a2 + -1(-3 + -5a + 2a2) = 0
3 + 7a + 2a2 + (-3 * -1 + -5a * -1 + 2a2 * -1) = 0
3 + 7a + 2a2 + (3 + 5a + -2a2) = 0

Reorder the terms:
3 + 3 + 7a + 5a + 2a2 + -2a2 = 0

Combine like terms: 3 + 3 = 6
6 + 7a + 5a + 2a2 + -2a2 = 0

Combine like terms: 7a + 5a = 12a
6 + 12a + 2a2 + -2a2 = 0

Combine like terms: 2a2 + -2a2 = 0
6 + 12a + 0 = 0
6 + 12a = 0

Solving
6 + 12a = 0

Solving for variable 'a'.

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

Add '-6' to each side of the equation.
6 + -6 + 12a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 12a = 0 + -6
12a = 0 + -6

Combine like terms: 0 + -6 = -6
12a = -6

Divide each side by '12'.
a = -0.5

Simplifying
a = -0.5