p^2+14p-61=-10

Solution for p^2+14p-61=-10 equation:

Simplifying
p2 + 14p + -61 = -10

Reorder the terms:
-61 + 14p + p2 = -10

Solving
-61 + 14p + p2 = -10

Solving for variable 'p'.

Reorder the terms:
-61 + 10 + 14p + p2 = -10 + 10

Combine like terms: -61 + 10 = -51
-51 + 14p + p2 = -10 + 10

Combine like terms: -10 + 10 = 0
-51 + 14p + p2 = 0

Factor a trinomial.
(-17 + -1p)(3 + -1p) = 0

Subproblem 1
Set the factor '(-17 + -1p)' equal to zero and attempt to solve:

Simplifying
-17 + -1p = 0

Solving
-17 + -1p = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1p = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1p = 0 + 17
-1p = 0 + 17

Combine like terms: 0 + 17 = 17
-1p = 17

Divide each side by '-1'.
p = -17

Simplifying
p = -17
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 = {-17, 3}