(p-4)(2p+1)=0

Solution for (p-4)(2p+1)=0 equation:

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

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

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

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

Combine like terms: -8p + 1p = -7p
(-4 + -7p + 2p2) = 0

Solving
-4 + -7p + 2p2 = 0

Solving for variable 'p'.

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

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

Simplifying
4 + -1p = 0

Solving
4 + -1p = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1p = 0 + -4

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

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

Divide each side by '-1'.
p = 4

Simplifying
p = 4
Solution
p = {-0.5, 4}