(x+9)(x-5)=(2x+7)(x-5)

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Solution for (x+9)(x-5)=(2x+7)(x-5) equation: 


Simplifying
(x + 9)(x + -5) = (2x + 7)(x + -5)

Reorder the terms:
(9 + x)(x + -5) = (2x + 7)(x + -5)

Reorder the terms:
(9 + x)(-5 + x) = (2x + 7)(x + -5)

Multiply (9 + x) * (-5 + x)
(9(-5 + x) + x(-5 + x)) = (2x + 7)(x + -5)
((-5 * 9 + x * 9) + x(-5 + x)) = (2x + 7)(x + -5)
((-45 + 9x) + x(-5 + x)) = (2x + 7)(x + -5)
(-45 + 9x + (-5 * x + x * x)) = (2x + 7)(x + -5)
(-45 + 9x + (-5x + x2)) = (2x + 7)(x + -5)

Combine like terms: 9x + -5x = 4x
(-45 + 4x + x2) = (2x + 7)(x + -5)

Reorder the terms:
-45 + 4x + x2 = (7 + 2x)(x + -5)

Reorder the terms:
-45 + 4x + x2 = (7 + 2x)(-5 + x)

Multiply (7 + 2x) * (-5 + x)
-45 + 4x + x2 = (7(-5 + x) + 2x * (-5 + x))
-45 + 4x + x2 = ((-5 * 7 + x * 7) + 2x * (-5 + x))
-45 + 4x + x2 = ((-35 + 7x) + 2x * (-5 + x))
-45 + 4x + x2 = (-35 + 7x + (-5 * 2x + x * 2x))
-45 + 4x + x2 = (-35 + 7x + (-10x + 2x2))

Combine like terms: 7x + -10x = -3x
-45 + 4x + x2 = (-35 + -3x + 2x2)

Solving
-45 + 4x + x2 = -35 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-45 + 35 + 4x + 3x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Combine like terms: -45 + 35 = -10
-10 + 4x + 3x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Combine like terms: 4x + 3x = 7x
-10 + 7x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-10 + 7x + -1x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Reorder the terms:
-10 + 7x + -1x2 = -35 + 35 + -3x + 3x + 2x2 + -2x2

Combine like terms: -35 + 35 = 0
-10 + 7x + -1x2 = 0 + -3x + 3x + 2x2 + -2x2
-10 + 7x + -1x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
-10 + 7x + -1x2 = 0 + 2x2 + -2x2
-10 + 7x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10 + 7x + -1x2 = 0

Factor a trinomial.
(-5 + x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {5, 2}

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