5p^2+25p=120

Solution for 5p^2+25p=120 equation:

Simplifying
5p2 + 25p = 120

Reorder the terms:
25p + 5p2 = 120

Solving
25p + 5p2 = 120

Solving for variable 'p'.

Reorder the terms:
-120 + 25p + 5p2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 25p + 5p2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-24 + 5p + p2) = 0

Factor a trinomial.
5((-8 + -1p)(3 + -1p)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-8 + -1p)' equal to zero and attempt to solve:

Simplifying
-8 + -1p = 0

Solving
-8 + -1p = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1p = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1p = 0 + 8
-1p = 0 + 8

Combine like terms: 0 + 8 = 8
-1p = 8

Divide each side by '-1'.
p = -8

Simplifying
p = -8
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 = {-8, 3}