4p^2+4p-48=0

Solution for 4p^2+4p-48=0 equation:

Simplifying
4p2 + 4p + -48 = 0

Reorder the terms:
-48 + 4p + 4p2 = 0

Solving
-48 + 4p + 4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + p + p2) = 0

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

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

Simplifying
3 + -1p = 0

Solving
3 + -1p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-4, 3}