5p(p-5)=30

Solution for 5p(p-5)=30 equation:

Simplifying
5p(p + -5) = 30

Reorder the terms:
5p(-5 + p) = 30
(-5 * 5p + p * 5p) = 30
(-25p + 5p2) = 30

Solving
-25p + 5p2 = 30

Solving for variable 'p'.

Reorder the terms:
-30 + -25p + 5p2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -25p + 5p2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + -5p + p2) = 0

Factor a trinomial.
5((-1 + -1p)(6 + -1p)) = 0

Ignore the factor 5.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1p)' equal to zero and attempt to solve:

Simplifying
6 + -1p = 0

Solving
6 + -1p = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1p = 0 + -6
-1p = 0 + -6

Combine like terms: 0 + -6 = -6
-1p = -6

Divide each side by '-1'.
p = 6

Simplifying
p = 6
Solution
p = {-1, 6}