p(7-p)=10

Solution for p(7-p)=10 equation:

Simplifying
p(7 + -1p) = 10
(7 * p + -1p * p) = 10
(7p + -1p2) = 10

Solving
7p + -1p2 = 10

Solving for variable 'p'.

Reorder the terms:
-10 + 7p + -1p2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 7p + -1p2 = 0

Factor a trinomial.
(-5 + p)(2 + -1p) = 0

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

Simplifying
-5 + p = 0

Solving
-5 + p = 0

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

Add '5' to each side of the equation.
-5 + 5 + p = 0 + 5

Combine like terms: -5 + 5 = 0
0 + p = 0 + 5
p = 0 + 5

Combine like terms: 0 + 5 = 5
p = 5

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

Simplifying
2 + -1p = 0

Solving
2 + -1p = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Solution
p = {5, 2}