(2+8p)(2-10p)=0

Solution for (2+8p)(2-10p)=0 equation:

Simplifying
(2 + 8p)(2 + -10p) = 0

Multiply (2 + 8p) * (2 + -10p)
(2(2 + -10p) + 8p * (2 + -10p)) = 0
((2 * 2 + -10p * 2) + 8p * (2 + -10p)) = 0
((4 + -20p) + 8p * (2 + -10p)) = 0
(4 + -20p + (2 * 8p + -10p * 8p)) = 0
(4 + -20p + (16p + -80p2)) = 0

Combine like terms: -20p + 16p = -4p
(4 + -4p + -80p2) = 0

Solving
4 + -4p + -80p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -1p + -20p2) = 0

Factor a trinomial.
4((1 + -5p)(1 + 4p)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -5p)' equal to zero and attempt to solve:

Simplifying
1 + -5p = 0

Solving
1 + -5p = 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 + -5p = 0 + -1

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

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

Divide each side by '-5'.
p = 0.2

Simplifying
p = 0.2
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 = {0.2, -0.25}