(2p+6)(8p+3)=

Solution for (2p+6)(8p+3)= equation:

Simplifying
(2p + 6)(8p + 3) = 0

Reorder the terms:
(6 + 2p)(8p + 3) = 0

Reorder the terms:
(6 + 2p)(3 + 8p) = 0

Multiply (6 + 2p) * (3 + 8p)
(6(3 + 8p) + 2p * (3 + 8p)) = 0
((3 * 6 + 8p * 6) + 2p * (3 + 8p)) = 0
((18 + 48p) + 2p * (3 + 8p)) = 0
(18 + 48p + (3 * 2p + 8p * 2p)) = 0
(18 + 48p + (6p + 16p2)) = 0

Combine like terms: 48p + 6p = 54p
(18 + 54p + 16p2) = 0

Solving
18 + 54p + 16p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 27p + 8p2) = 0

Factor a trinomial.
2((3 + p)(3 + 8p)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + p)' equal to zero and attempt to solve:

Simplifying
3 + p = 0

Solving
3 + p = 0

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

Add '-3' to each side of the equation.
3 + -3 + p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + p = 0 + -3
p = 0 + -3

Combine like terms: 0 + -3 = -3
p = -3

Simplifying
p = -3
Subproblem 2
Set the factor '(3 + 8p)' equal to zero and attempt to solve:

Simplifying
3 + 8p = 0

Solving
3 + 8p = 0

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

Add '-3' to each side of the equation.
3 + -3 + 8p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8p = 0 + -3
8p = 0 + -3

Combine like terms: 0 + -3 = -3
8p = -3

Divide each side by '8'.
p = -0.375

Simplifying
p = -0.375
Solution
p = {-3, -0.375}