(p+6)(p+5)=20p+40

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Solution for (p+6)(p+5)=20p+40 equation: 


Simplifying
(p + 6)(p + 5) = 20p + 40

Reorder the terms:
(6 + p)(p + 5) = 20p + 40

Reorder the terms:
(6 + p)(5 + p) = 20p + 40

Multiply (6 + p) * (5 + p)
(6(5 + p) + p(5 + p)) = 20p + 40
((5 * 6 + p * 6) + p(5 + p)) = 20p + 40
((30 + 6p) + p(5 + p)) = 20p + 40
(30 + 6p + (5 * p + p * p)) = 20p + 40
(30 + 6p + (5p + p2)) = 20p + 40

Combine like terms: 6p + 5p = 11p
(30 + 11p + p2) = 20p + 40

Reorder the terms:
30 + 11p + p2 = 40 + 20p

Solving
30 + 11p + p2 = 40 + 20p

Solving for variable 'p'.

Reorder the terms:
30 + -40 + 11p + -20p + p2 = 40 + 20p + -40 + -20p

Combine like terms: 30 + -40 = -10
-10 + 11p + -20p + p2 = 40 + 20p + -40 + -20p

Combine like terms: 11p + -20p = -9p
-10 + -9p + p2 = 40 + 20p + -40 + -20p

Reorder the terms:
-10 + -9p + p2 = 40 + -40 + 20p + -20p

Combine like terms: 40 + -40 = 0
-10 + -9p + p2 = 0 + 20p + -20p
-10 + -9p + p2 = 20p + -20p

Combine like terms: 20p + -20p = 0
-10 + -9p + p2 = 0

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


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

Simplifying
-1 + -1p = 0

Solving
-1 + -1p = 0

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

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

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

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

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

Simplifying
p = -1

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 = {-1, 10}

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