p(p+3)-10=0

Solution for p(p+3)-10=0 equation:

Simplifying
p(p + 3) + -10 = 0

Reorder the terms:
p(3 + p) + -10 = 0
(3 * p + p * p) + -10 = 0
(3p + p2) + -10 = 0

Reorder the terms:
-10 + 3p + p2 = 0

Solving
-10 + 3p + p2 = 0

Solving for variable 'p'.

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

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

Simplifying
-5 + -1p = 0

Solving
-5 + -1p = 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 + -1p = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1p = 0 + 5
-1p = 0 + 5

Combine like terms: 0 + 5 = 5
-1p = 5

Divide each side by '-1'.
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}