p^2+2p-31=4

Solution for p^2+2p-31=4 equation:

Simplifying
p2 + 2p + -31 = 4

Reorder the terms:
-31 + 2p + p2 = 4

Solving
-31 + 2p + p2 = 4

Solving for variable 'p'.

Reorder the terms:
-31 + -4 + 2p + p2 = 4 + -4

Combine like terms: -31 + -4 = -35
-35 + 2p + p2 = 4 + -4

Combine like terms: 4 + -4 = 0
-35 + 2p + p2 = 0

Factor a trinomial.
(-7 + -1p)(5 + -1p) = 0

Subproblem 1
Set the factor '(-7 + -1p)' equal to zero and attempt to solve:

Simplifying
-7 + -1p = 0

Solving
-7 + -1p = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1p = 0 + 7

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

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

Divide each side by '-1'.
p = -7

Simplifying
p = -7
Subproblem 2
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
Solution
p = {-7, 5}