2p(p+1)+2p(p+1)=8

Solution for 2p(p+1)+2p(p+1)=8 equation:

Simplifying
2p(p + 1) + 2p(p + 1) = 8

Reorder the terms:
2p(1 + p) + 2p(p + 1) = 8
(1 * 2p + p * 2p) + 2p(p + 1) = 8
(2p + 2p2) + 2p(p + 1) = 8

Reorder the terms:
2p + 2p2 + 2p(1 + p) = 8
2p + 2p2 + (1 * 2p + p * 2p) = 8
2p + 2p2 + (2p + 2p2) = 8

Reorder the terms:
2p + 2p + 2p2 + 2p2 = 8

Combine like terms: 2p + 2p = 4p
4p + 2p2 + 2p2 = 8

Combine like terms: 2p2 + 2p2 = 4p2
4p + 4p2 = 8

Solving
4p + 4p2 = 8

Solving for variable 'p'.

Reorder the terms:
-8 + 4p + 4p2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 4p + 4p2 = 0

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

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

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

Simplifying
-2 + -1p = 0

Solving
-2 + -1p = 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 + -1p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1p = 0 + 2
-1p = 0 + 2

Combine like terms: 0 + 2 = 2
-1p = 2

Divide each side by '-1'.
p = -2

Simplifying
p = -2
Subproblem 2
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
Solution
p = {-2, 1}