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

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

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

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

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

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

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

Solving
-1 + 1p + 2p2 = 0

Solving for variable 'p'.

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

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

Simplifying
-1 + -1p = 0

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

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

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

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

Simplifying
p = -1
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 = {-1, 0.5}