(2p+3)(2p+3)=16

Solution for (2p+3)(2p+3)=16 equation:

Simplifying
(2p + 3)(2p + 3) = 16

Reorder the terms:
(3 + 2p)(2p + 3) = 16

Reorder the terms:
(3 + 2p)(3 + 2p) = 16

Multiply (3 + 2p) * (3 + 2p)
(3(3 + 2p) + 2p * (3 + 2p)) = 16
((3 * 3 + 2p * 3) + 2p * (3 + 2p)) = 16
((9 + 6p) + 2p * (3 + 2p)) = 16
(9 + 6p + (3 * 2p + 2p * 2p)) = 16
(9 + 6p + (6p + 4p2)) = 16

Combine like terms: 6p + 6p = 12p
(9 + 12p + 4p2) = 16

Solving
9 + 12p + 4p2 = 16

Solving for variable 'p'.

Reorder the terms:
9 + -16 + 12p + 4p2 = 16 + -16

Combine like terms: 9 + -16 = -7
-7 + 12p + 4p2 = 16 + -16

Combine like terms: 16 + -16 = 0
-7 + 12p + 4p2 = 0

Factor a trinomial.
(-7 + -2p)(1 + -2p) = 0

Subproblem 1
Set the factor '(-7 + -2p)' equal to zero and attempt to solve:

Simplifying
-7 + -2p = 0

Solving
-7 + -2p = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2p = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2p = 0 + 7
-2p = 0 + 7

Combine like terms: 0 + 7 = 7
-2p = 7

Divide each side by '-2'.
p = -3.5

Simplifying
p = -3.5
Subproblem 2
Set the factor '(1 + -2p)' equal to zero and attempt to solve:

Simplifying
1 + -2p = 0

Solving
1 + -2p = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2p = 0 + -1
-2p = 0 + -1

Combine like terms: 0 + -1 = -1
-2p = -1

Divide each side by '-2'.
p = 0.5

Simplifying
p = 0.5
Solution
p = {-3.5, 0.5}