(8p-4)(5p+2)=

Solution for (8p-4)(5p+2)= equation:

Simplifying
(8p + -4)(5p + 2) = 0

Reorder the terms:
(-4 + 8p)(5p + 2) = 0

Reorder the terms:
(-4 + 8p)(2 + 5p) = 0

Multiply (-4 + 8p) * (2 + 5p)
(-4(2 + 5p) + 8p * (2 + 5p)) = 0
((2 * -4 + 5p * -4) + 8p * (2 + 5p)) = 0
((-8 + -20p) + 8p * (2 + 5p)) = 0
(-8 + -20p + (2 * 8p + 5p * 8p)) = 0
(-8 + -20p + (16p + 40p2)) = 0

Combine like terms: -20p + 16p = -4p
(-8 + -4p + 40p2) = 0

Solving
-8 + -4p + 40p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -1p + 10p2) = 0

Factor a trinomial.
4((-2 + -5p)(1 + -2p)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + -5p)' equal to zero and attempt to solve:

Simplifying
-2 + -5p = 0

Solving
-2 + -5p = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5p = 0 + 2
-5p = 0 + 2

Combine like terms: 0 + 2 = 2
-5p = 2

Divide each side by '-5'.
p = -0.4

Simplifying
p = -0.4
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 = {-0.4, 0.5}