(p+4)(p+2)=35

Solution for (p+4)(p+2)=35 equation:

Simplifying
(p + 4)(p + 2) = 35

Reorder the terms:
(4 + p)(p + 2) = 35

Reorder the terms:
(4 + p)(2 + p) = 35

Multiply (4 + p) * (2 + p)
(4(2 + p) + p(2 + p)) = 35
((2 * 4 + p * 4) + p(2 + p)) = 35
((8 + 4p) + p(2 + p)) = 35
(8 + 4p + (2 * p + p * p)) = 35
(8 + 4p + (2p + p2)) = 35

Combine like terms: 4p + 2p = 6p
(8 + 6p + p2) = 35

Solving
8 + 6p + p2 = 35

Solving for variable 'p'.

Reorder the terms:
8 + -35 + 6p + p2 = 35 + -35

Combine like terms: 8 + -35 = -27
-27 + 6p + p2 = 35 + -35

Combine like terms: 35 + -35 = 0
-27 + 6p + p2 = 0

Factor a trinomial.
(-9 + -1p)(3 + -1p) = 0

Subproblem 1
Set the factor '(-9 + -1p)' equal to zero and attempt to solve:

Simplifying
-9 + -1p = 0

Solving
-9 + -1p = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1p = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1p = 0 + 9
-1p = 0 + 9

Combine like terms: 0 + 9 = 9
-1p = 9

Divide each side by '-1'.
p = -9

Simplifying
p = -9
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 = {-9, 3}