p^2+6p-61=-6

Solution for p^2+6p-61=-6 equation:

Simplifying
p2 + 6p + -61 = -6

Reorder the terms:
-61 + 6p + p2 = -6

Solving
-61 + 6p + p2 = -6

Solving for variable 'p'.

Reorder the terms:
-61 + 6 + 6p + p2 = -6 + 6

Combine like terms: -61 + 6 = -55
-55 + 6p + p2 = -6 + 6

Combine like terms: -6 + 6 = 0
-55 + 6p + p2 = 0

Factor a trinomial.
(-11 + -1p)(5 + -1p) = 0

Subproblem 1
Set the factor '(-11 + -1p)' equal to zero and attempt to solve:

Simplifying
-11 + -1p = 0

Solving
-11 + -1p = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1p = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1p = 0 + 11
-1p = 0 + 11

Combine like terms: 0 + 11 = 11
-1p = 11

Divide each side by '-1'.
p = -11

Simplifying
p = -11
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 = {-11, 5}