5p(p-7)=-60

Solution for 5p(p-7)=-60 equation:

Simplifying
5p(p + -7) = -60

Reorder the terms:
5p(-7 + p) = -60
(-7 * 5p + p * 5p) = -60
(-35p + 5p2) = -60

Solving
-35p + 5p2 = -60

Solving for variable 'p'.

Reorder the terms:
60 + -35p + 5p2 = -60 + 60

Combine like terms: -60 + 60 = 0
60 + -35p + 5p2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(12 + -7p + p2) = 0

Factor a trinomial.
5((3 + -1p)(4 + -1p)) = 0

Ignore the factor 5.
Subproblem 1
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
Subproblem 2
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
Solution
p = {3, 4}