(x+8)(x+5)=x^2+px+40

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Solution for (x+8)(x+5)=x^2+px+40 equation: 


Simplifying
(x + 8)(x + 5) = x2 + px + 40

Reorder the terms:
(8 + x)(x + 5) = x2 + px + 40

Reorder the terms:
(8 + x)(5 + x) = x2 + px + 40

Multiply (8 + x) * (5 + x)
(8(5 + x) + x(5 + x)) = x2 + px + 40
((5 * 8 + x * 8) + x(5 + x)) = x2 + px + 40
((40 + 8x) + x(5 + x)) = x2 + px + 40
(40 + 8x + (5 * x + x * x)) = x2 + px + 40
(40 + 8x + (5x + x2)) = x2 + px + 40

Combine like terms: 8x + 5x = 13x
(40 + 13x + x2) = x2 + px + 40

Reorder the terms:
40 + 13x + x2 = 40 + px + x2

Add '-40' to each side of the equation.
40 + 13x + -40 + x2 = 40 + px + -40 + x2

Reorder the terms:
40 + -40 + 13x + x2 = 40 + px + -40 + x2

Combine like terms: 40 + -40 = 0
0 + 13x + x2 = 40 + px + -40 + x2
13x + x2 = 40 + px + -40 + x2

Reorder the terms:
13x + x2 = 40 + -40 + px + x2

Combine like terms: 40 + -40 = 0
13x + x2 = 0 + px + x2
13x + x2 = px + x2

Add '-1x2' to each side of the equation.
13x + x2 + -1x2 = px + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
13x + 0 = px + x2 + -1x2
13x = px + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
13x = px + 0
13x = px

Solving
13x = px

Solving for variable 'x'.

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

Add '-1px' to each side of the equation.
-1px + 13x = px + -1px

Combine like terms: px + -1px = 0
-1px + 13x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1p + 13) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-1p + 13)' equal to zero and attempt to solve:

Simplifying
-1p + 13 = 0

Reorder the terms:
13 + -1p = 0

Solving
13 + -1p = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1p = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1p = 0 + -13
-1p = 0 + -13

Combine like terms: 0 + -13 = -13
-1p = -13

Add 'p' to each side of the equation.
-1p + p = -13 + p

Combine like terms: -1p + p = 0
0 = -13 + p

Simplifying
0 = -13 + p

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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