(2p+2)(5p+4)=0

Solution for (2p+2)(5p+4)=0 equation:

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

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

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

Multiply (2 + 2p) * (4 + 5p)
(2(4 + 5p) + 2p * (4 + 5p)) = 0
((4 * 2 + 5p * 2) + 2p * (4 + 5p)) = 0
((8 + 10p) + 2p * (4 + 5p)) = 0
(8 + 10p + (4 * 2p + 5p * 2p)) = 0
(8 + 10p + (8p + 10p2)) = 0

Combine like terms: 10p + 8p = 18p
(8 + 18p + 10p2) = 0

Solving
8 + 18p + 10p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 9p + 5p2) = 0

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

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

Simplifying
1 + p = 0

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

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

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

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

Simplifying
4 + 5p = 0

Solving
4 + 5p = 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 + 5p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5p = 0 + -4
5p = 0 + -4

Combine like terms: 0 + -4 = -4
5p = -4

Divide each side by '5'.
p = -0.8

Simplifying
p = -0.8
Solution
p = {-1, -0.8}