p^2+5p-78=6

Solution for p^2+5p-78=6 equation:

Simplifying
p2 + 5p + -78 = 6

Reorder the terms:
-78 + 5p + p2 = 6

Solving
-78 + 5p + p2 = 6

Solving for variable 'p'.

Reorder the terms:
-78 + -6 + 5p + p2 = 6 + -6

Combine like terms: -78 + -6 = -84
-84 + 5p + p2 = 6 + -6

Combine like terms: 6 + -6 = 0
-84 + 5p + p2 = 0

Factor a trinomial.
(-12 + -1p)(7 + -1p) = 0

Subproblem 1
Set the factor '(-12 + -1p)' equal to zero and attempt to solve:

Simplifying
-12 + -1p = 0

Solving
-12 + -1p = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1p = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1p = 0 + 12
-1p = 0 + 12

Combine like terms: 0 + 12 = 12
-1p = 12

Divide each side by '-1'.
p = -12

Simplifying
p = -12
Subproblem 2
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
Solution
p = {-12, 7}