3p+3=p^2-51

Solution for 3p+3=p^2-51 equation:

Simplifying
3p + 3 = p2 + -51

Reorder the terms:
3 + 3p = p2 + -51

Reorder the terms:
3 + 3p = -51 + p2

Solving
3 + 3p = -51 + p2

Solving for variable 'p'.

Reorder the terms:
3 + 51 + 3p + -1p2 = -51 + p2 + 51 + -1p2

Combine like terms: 3 + 51 = 54
54 + 3p + -1p2 = -51 + p2 + 51 + -1p2

Reorder the terms:
54 + 3p + -1p2 = -51 + 51 + p2 + -1p2

Combine like terms: -51 + 51 = 0
54 + 3p + -1p2 = 0 + p2 + -1p2
54 + 3p + -1p2 = p2 + -1p2

Combine like terms: p2 + -1p2 = 0
54 + 3p + -1p2 = 0

Factor a trinomial.
(9 + -1p)(6 + p) = 0

Subproblem 1
Set the factor '(9 + -1p)' equal to zero and attempt to solve:

Simplifying
9 + -1p = 0

Solving
9 + -1p = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1p = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1p = 0 + -9
-1p = 0 + -9

Combine like terms: 0 + -9 = -9
-1p = -9

Divide each side by '-1'.
p = 9

Simplifying
p = 9
Subproblem 2
Set the factor '(6 + p)' equal to zero and attempt to solve:

Simplifying
6 + p = 0

Solving
6 + p = 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 + p = 0 + -6

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

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

Simplifying
p = -6
Solution
p = {9, -6}