5*(x+13)=(x+4)(x+5)

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Solution for 5*(x+13)=(x+4)(x+5) equation: 


Simplifying
5(x + 13) = (x + 4)(x + 5)

Reorder the terms:
5(13 + x) = (x + 4)(x + 5)
(13 * 5 + x * 5) = (x + 4)(x + 5)
(65 + 5x) = (x + 4)(x + 5)

Reorder the terms:
65 + 5x = (4 + x)(x + 5)

Reorder the terms:
65 + 5x = (4 + x)(5 + x)

Multiply (4 + x) * (5 + x)
65 + 5x = (4(5 + x) + x(5 + x))
65 + 5x = ((5 * 4 + x * 4) + x(5 + x))
65 + 5x = ((20 + 4x) + x(5 + x))
65 + 5x = (20 + 4x + (5 * x + x * x))
65 + 5x = (20 + 4x + (5x + x2))

Combine like terms: 4x + 5x = 9x
65 + 5x = (20 + 9x + x2)

Solving
65 + 5x = 20 + 9x + x2

Solving for variable 'x'.

Reorder the terms:
65 + -20 + 5x + -9x + -1x2 = 20 + 9x + x2 + -20 + -9x + -1x2

Combine like terms: 65 + -20 = 45
45 + 5x + -9x + -1x2 = 20 + 9x + x2 + -20 + -9x + -1x2

Combine like terms: 5x + -9x = -4x
45 + -4x + -1x2 = 20 + 9x + x2 + -20 + -9x + -1x2

Reorder the terms:
45 + -4x + -1x2 = 20 + -20 + 9x + -9x + x2 + -1x2

Combine like terms: 20 + -20 = 0
45 + -4x + -1x2 = 0 + 9x + -9x + x2 + -1x2
45 + -4x + -1x2 = 9x + -9x + x2 + -1x2

Combine like terms: 9x + -9x = 0
45 + -4x + -1x2 = 0 + x2 + -1x2
45 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
45 + -4x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(9 + x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

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

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Solution
x = {5, -9}

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