(p-3)(p-4)=42

Solution for (p-3)(p-4)=42 equation:

Simplifying
(p + -3)(p + -4) = 42

Reorder the terms:
(-3 + p)(p + -4) = 42

Reorder the terms:
(-3 + p)(-4 + p) = 42

Multiply (-3 + p) * (-4 + p)
(-3(-4 + p) + p(-4 + p)) = 42
((-4 * -3 + p * -3) + p(-4 + p)) = 42
((12 + -3p) + p(-4 + p)) = 42
(12 + -3p + (-4 * p + p * p)) = 42
(12 + -3p + (-4p + p2)) = 42

Combine like terms: -3p + -4p = -7p
(12 + -7p + p2) = 42

Solving
12 + -7p + p2 = 42

Solving for variable 'p'.

Reorder the terms:
12 + -42 + -7p + p2 = 42 + -42

Combine like terms: 12 + -42 = -30
-30 + -7p + p2 = 42 + -42

Combine like terms: 42 + -42 = 0
-30 + -7p + p2 = 0

Factor a trinomial.
(-3 + -1p)(10 + -1p) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(10 + -1p)' equal to zero and attempt to solve:

Simplifying
10 + -1p = 0

Solving
10 + -1p = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1p = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1p = 0 + -10
-1p = 0 + -10

Combine like terms: 0 + -10 = -10
-1p = -10

Divide each side by '-1'.
p = 10

Simplifying
p = 10
Solution
p = {-3, 10}