(p-1)(p-6)=126

Solution for (p-1)(p-6)=126 equation:

Simplifying
(p + -1)(p + -6) = 126

Reorder the terms:
(-1 + p)(p + -6) = 126

Reorder the terms:
(-1 + p)(-6 + p) = 126

Multiply (-1 + p) * (-6 + p)
(-1(-6 + p) + p(-6 + p)) = 126
((-6 * -1 + p * -1) + p(-6 + p)) = 126
((6 + -1p) + p(-6 + p)) = 126
(6 + -1p + (-6 * p + p * p)) = 126
(6 + -1p + (-6p + p2)) = 126

Combine like terms: -1p + -6p = -7p
(6 + -7p + p2) = 126

Solving
6 + -7p + p2 = 126

Solving for variable 'p'.

Reorder the terms:
6 + -126 + -7p + p2 = 126 + -126

Combine like terms: 6 + -126 = -120
-120 + -7p + p2 = 126 + -126

Combine like terms: 126 + -126 = 0
-120 + -7p + p2 = 0

Factor a trinomial.
(-8 + -1p)(15 + -1p) = 0

Subproblem 1
Set the factor '(-8 + -1p)' equal to zero and attempt to solve:

Simplifying
-8 + -1p = 0

Solving
-8 + -1p = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1p = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1p = 0 + 8
-1p = 0 + 8

Combine like terms: 0 + 8 = 8
-1p = 8

Divide each side by '-1'.
p = -8

Simplifying
p = -8
Subproblem 2
Set the factor '(15 + -1p)' equal to zero and attempt to solve:

Simplifying
15 + -1p = 0

Solving
15 + -1p = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1p = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1p = 0 + -15
-1p = 0 + -15

Combine like terms: 0 + -15 = -15
-1p = -15

Divide each side by '-1'.
p = 15

Simplifying
p = 15
Solution
p = {-8, 15}