p(p+3)=5p+3

Solution for p(p+3)=5p+3 equation:

Simplifying
p(p + 3) = 5p + 3

Reorder the terms:
p(3 + p) = 5p + 3
(3 * p + p * p) = 5p + 3
(3p + p2) = 5p + 3

Reorder the terms:
3p + p2 = 3 + 5p

Solving
3p + p2 = 3 + 5p

Solving for variable 'p'.

Reorder the terms:
-3 + 3p + -5p + p2 = 3 + 5p + -3 + -5p

Combine like terms: 3p + -5p = -2p
-3 + -2p + p2 = 3 + 5p + -3 + -5p

Reorder the terms:
-3 + -2p + p2 = 3 + -3 + 5p + -5p

Combine like terms: 3 + -3 = 0
-3 + -2p + p2 = 0 + 5p + -5p
-3 + -2p + p2 = 5p + -5p

Combine like terms: 5p + -5p = 0
-3 + -2p + p2 = 0

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

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 '(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 = {-1, 3}