(p-5)(2p-1)=0

Solution for (p-5)(2p-1)=0 equation:

Simplifying
(p + -5)(2p + -1) = 0

Reorder the terms:
(-5 + p)(2p + -1) = 0

Reorder the terms:
(-5 + p)(-1 + 2p) = 0

Multiply (-5 + p) * (-1 + 2p)
(-5(-1 + 2p) + p(-1 + 2p)) = 0
((-1 * -5 + 2p * -5) + p(-1 + 2p)) = 0
((5 + -10p) + p(-1 + 2p)) = 0
(5 + -10p + (-1 * p + 2p * p)) = 0
(5 + -10p + (-1p + 2p2)) = 0

Combine like terms: -10p + -1p = -11p
(5 + -11p + 2p2) = 0

Solving
5 + -11p + 2p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(1 + -2p)(5 + -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 '(5 + -1p)' equal to zero and attempt to solve:

Simplifying
5 + -1p = 0

Solving
5 + -1p = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1p = 0 + -5
-1p = 0 + -5

Combine like terms: 0 + -5 = -5
-1p = -5

Divide each side by '-1'.
p = 5

Simplifying
p = 5
Solution
p = {0.5, 5}