2p(p+4)+(p-3)(p+4)=

Solution for 2p(p+4)+(p-3)(p+4)= equation:

Simplifying
2p(p + 4) + (p + -3)(p + 4) = 0

Reorder the terms:
2p(4 + p) + (p + -3)(p + 4) = 0
(4 * 2p + p * 2p) + (p + -3)(p + 4) = 0
(8p + 2p2) + (p + -3)(p + 4) = 0

Reorder the terms:
8p + 2p2 + (-3 + p)(p + 4) = 0

Reorder the terms:
8p + 2p2 + (-3 + p)(4 + p) = 0

Multiply (-3 + p) * (4 + p)
8p + 2p2 + (-3(4 + p) + p(4 + p)) = 0
8p + 2p2 + ((4 * -3 + p * -3) + p(4 + p)) = 0
8p + 2p2 + ((-12 + -3p) + p(4 + p)) = 0
8p + 2p2 + (-12 + -3p + (4 * p + p * p)) = 0
8p + 2p2 + (-12 + -3p + (4p + p2)) = 0

Combine like terms: -3p + 4p = 1p
8p + 2p2 + (-12 + 1p + p2) = 0

Reorder the terms:
-12 + 8p + 1p + 2p2 + p2 = 0

Combine like terms: 8p + 1p = 9p
-12 + 9p + 2p2 + p2 = 0

Combine like terms: 2p2 + p2 = 3p2
-12 + 9p + 3p2 = 0

Solving
-12 + 9p + 3p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 3p + p2) = 0

Factor a trinomial.
3((-4 + -1p)(1 + -1p)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1p)' equal to zero and attempt to solve:

Simplifying
-4 + -1p = 0

Solving
-4 + -1p = 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 + -1p = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1p = 0 + 4
-1p = 0 + 4

Combine like terms: 0 + 4 = 4
-1p = 4

Divide each side by '-1'.
p = -4

Simplifying
p = -4
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 = {-4, 1}