(2p+3)(4p+1)=

Solution for (2p+3)(4p+1)= equation:

Simplifying
(2p + 3)(4p + 1) = 0

Reorder the terms:
(3 + 2p)(4p + 1) = 0

Reorder the terms:
(3 + 2p)(1 + 4p) = 0

Multiply (3 + 2p) * (1 + 4p)
(3(1 + 4p) + 2p * (1 + 4p)) = 0
((1 * 3 + 4p * 3) + 2p * (1 + 4p)) = 0
((3 + 12p) + 2p * (1 + 4p)) = 0
(3 + 12p + (1 * 2p + 4p * 2p)) = 0
(3 + 12p + (2p + 8p2)) = 0

Combine like terms: 12p + 2p = 14p
(3 + 14p + 8p2) = 0

Solving
3 + 14p + 8p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(3 + 2p)(1 + 4p) = 0

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

Simplifying
3 + 2p = 0

Solving
3 + 2p = 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 + 2p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2p = 0 + -3
2p = 0 + -3

Combine like terms: 0 + -3 = -3
2p = -3

Divide each side by '2'.
p = -1.5

Simplifying
p = -1.5
Subproblem 2
Set the factor '(1 + 4p)' equal to zero and attempt to solve:

Simplifying
1 + 4p = 0

Solving
1 + 4p = 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 + 4p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4p = 0 + -1
4p = 0 + -1

Combine like terms: 0 + -1 = -1
4p = -1

Divide each side by '4'.
p = -0.25

Simplifying
p = -0.25
Solution
p = {-1.5, -0.25}