(x-5)(x+2)=(x-9)(x+4)

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Solution for (x-5)(x+2)=(x-9)(x+4) equation: 


Simplifying
(x + -5)(x + 2) = (x + -9)(x + 4)

Reorder the terms:
(-5 + x)(x + 2) = (x + -9)(x + 4)

Reorder the terms:
(-5 + x)(2 + x) = (x + -9)(x + 4)

Multiply (-5 + x) * (2 + x)
(-5(2 + x) + x(2 + x)) = (x + -9)(x + 4)
((2 * -5 + x * -5) + x(2 + x)) = (x + -9)(x + 4)
((-10 + -5x) + x(2 + x)) = (x + -9)(x + 4)
(-10 + -5x + (2 * x + x * x)) = (x + -9)(x + 4)
(-10 + -5x + (2x + x2)) = (x + -9)(x + 4)

Combine like terms: -5x + 2x = -3x
(-10 + -3x + x2) = (x + -9)(x + 4)

Reorder the terms:
-10 + -3x + x2 = (-9 + x)(x + 4)

Reorder the terms:
-10 + -3x + x2 = (-9 + x)(4 + x)

Multiply (-9 + x) * (4 + x)
-10 + -3x + x2 = (-9(4 + x) + x(4 + x))
-10 + -3x + x2 = ((4 * -9 + x * -9) + x(4 + x))
-10 + -3x + x2 = ((-36 + -9x) + x(4 + x))
-10 + -3x + x2 = (-36 + -9x + (4 * x + x * x))
-10 + -3x + x2 = (-36 + -9x + (4x + x2))

Combine like terms: -9x + 4x = -5x
-10 + -3x + x2 = (-36 + -5x + x2)

Add '-1x2' to each side of the equation.
-10 + -3x + x2 + -1x2 = -36 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x + 0 = -36 + -5x + x2 + -1x2
-10 + -3x = -36 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x = -36 + -5x + 0
-10 + -3x = -36 + -5x

Solving
-10 + -3x = -36 + -5x

Solving for variable 'x'.

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

Add '5x' to each side of the equation.
-10 + -3x + 5x = -36 + -5x + 5x

Combine like terms: -3x + 5x = 2x
-10 + 2x = -36 + -5x + 5x

Combine like terms: -5x + 5x = 0
-10 + 2x = -36 + 0
-10 + 2x = -36

Add '10' to each side of the equation.
-10 + 10 + 2x = -36 + 10

Combine like terms: -10 + 10 = 0
0 + 2x = -36 + 10
2x = -36 + 10

Combine like terms: -36 + 10 = -26
2x = -26

Divide each side by '2'.
x = -13

Simplifying
x = -13

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