(x+9)(x-5)=(2x+8)(x-5)

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Solution for (x+9)(x-5)=(2x+8)(x-5) equation: 


Simplifying
(x + 9)(x + -5) = (2x + 8)(x + -5)

Reorder the terms:
(9 + x)(x + -5) = (2x + 8)(x + -5)

Reorder the terms:
(9 + x)(-5 + x) = (2x + 8)(x + -5)

Multiply (9 + x) * (-5 + x)
(9(-5 + x) + x(-5 + x)) = (2x + 8)(x + -5)
((-5 * 9 + x * 9) + x(-5 + x)) = (2x + 8)(x + -5)
((-45 + 9x) + x(-5 + x)) = (2x + 8)(x + -5)
(-45 + 9x + (-5 * x + x * x)) = (2x + 8)(x + -5)
(-45 + 9x + (-5x + x2)) = (2x + 8)(x + -5)

Combine like terms: 9x + -5x = 4x
(-45 + 4x + x2) = (2x + 8)(x + -5)

Reorder the terms:
-45 + 4x + x2 = (8 + 2x)(x + -5)

Reorder the terms:
-45 + 4x + x2 = (8 + 2x)(-5 + x)

Multiply (8 + 2x) * (-5 + x)
-45 + 4x + x2 = (8(-5 + x) + 2x * (-5 + x))
-45 + 4x + x2 = ((-5 * 8 + x * 8) + 2x * (-5 + x))
-45 + 4x + x2 = ((-40 + 8x) + 2x * (-5 + x))
-45 + 4x + x2 = (-40 + 8x + (-5 * 2x + x * 2x))
-45 + 4x + x2 = (-40 + 8x + (-10x + 2x2))

Combine like terms: 8x + -10x = -2x
-45 + 4x + x2 = (-40 + -2x + 2x2)

Solving
-45 + 4x + x2 = -40 + -2x + 2x2

Solving for variable 'x'.

Reorder the terms:
-45 + 40 + 4x + 2x + x2 + -2x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2

Combine like terms: -45 + 40 = -5
-5 + 4x + 2x + x2 + -2x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2

Combine like terms: 4x + 2x = 6x
-5 + 6x + x2 + -2x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-5 + 6x + -1x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2

Reorder the terms:
-5 + 6x + -1x2 = -40 + 40 + -2x + 2x + 2x2 + -2x2

Combine like terms: -40 + 40 = 0
-5 + 6x + -1x2 = 0 + -2x + 2x + 2x2 + -2x2
-5 + 6x + -1x2 = -2x + 2x + 2x2 + -2x2

Combine like terms: -2x + 2x = 0
-5 + 6x + -1x2 = 0 + 2x2 + -2x2
-5 + 6x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5 + 6x + -1x2 = 0

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


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

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Simplifying
x = 5

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {5, 1}

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