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

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

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

Reorder the terms for easier multiplication:
2(3a + 2p) + -1(a + p) * 2 = 0
(3a * 2 + 2p * 2) + -1(a + p) * 2 = 0
(6a + 4p) + -1(a + p) * 2 = 0

Reorder the terms for easier multiplication:
6a + 4p + -1 * 2(a + p) = 0

Multiply -1 * 2
6a + 4p + -2(a + p) = 0
6a + 4p + (a * -2 + p * -2) = 0
6a + 4p + (-2a + -2p) = 0

Reorder the terms:
6a + -2a + 4p + -2p = 0

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

Combine like terms: 4p + -2p = 2p
4a + 2p = 0

Solving
4a + 2p = 0

Solving for variable 'a'.

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

Add '-2p' to each side of the equation.
4a + 2p + -2p = 0 + -2p

Combine like terms: 2p + -2p = 0
4a + 0 = 0 + -2p
4a = 0 + -2p
Remove the zero:
4a = -2p

Divide each side by '4'.
a = -0.5p

Simplifying
a = -0.5p