(x-3)*(x-5)=(x+9)*(x+4)

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Solution for (x-3)*(x-5)=(x+9)*(x+4) equation: 


Simplifying
(x + -3)(x + -5) = (x + 9)(x + 4)

Reorder the terms:
(-3 + x)(x + -5) = (x + 9)(x + 4)

Reorder the terms:
(-3 + x)(-5 + x) = (x + 9)(x + 4)

Multiply (-3 + x) * (-5 + x)
(-3(-5 + x) + x(-5 + x)) = (x + 9)(x + 4)
((-5 * -3 + x * -3) + x(-5 + x)) = (x + 9)(x + 4)
((15 + -3x) + x(-5 + x)) = (x + 9)(x + 4)
(15 + -3x + (-5 * x + x * x)) = (x + 9)(x + 4)
(15 + -3x + (-5x + x2)) = (x + 9)(x + 4)

Combine like terms: -3x + -5x = -8x
(15 + -8x + x2) = (x + 9)(x + 4)

Reorder the terms:
15 + -8x + x2 = (9 + x)(x + 4)

Reorder the terms:
15 + -8x + x2 = (9 + x)(4 + x)

Multiply (9 + x) * (4 + x)
15 + -8x + x2 = (9(4 + x) + x(4 + x))
15 + -8x + x2 = ((4 * 9 + x * 9) + x(4 + x))
15 + -8x + x2 = ((36 + 9x) + x(4 + x))
15 + -8x + x2 = (36 + 9x + (4 * x + x * x))
15 + -8x + x2 = (36 + 9x + (4x + x2))

Combine like terms: 9x + 4x = 13x
15 + -8x + x2 = (36 + 13x + x2)

Add '-1x2' to each side of the equation.
15 + -8x + x2 + -1x2 = 36 + 13x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + -8x + 0 = 36 + 13x + x2 + -1x2
15 + -8x = 36 + 13x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + -8x = 36 + 13x + 0
15 + -8x = 36 + 13x

Solving
15 + -8x = 36 + 13x

Solving for variable 'x'.

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

Add '-13x' to each side of the equation.
15 + -8x + -13x = 36 + 13x + -13x

Combine like terms: -8x + -13x = -21x
15 + -21x = 36 + 13x + -13x

Combine like terms: 13x + -13x = 0
15 + -21x = 36 + 0
15 + -21x = 36

Add '-15' to each side of the equation.
15 + -15 + -21x = 36 + -15

Combine like terms: 15 + -15 = 0
0 + -21x = 36 + -15
-21x = 36 + -15

Combine like terms: 36 + -15 = 21
-21x = 21

Divide each side by '-21'.
x = -1

Simplifying
x = -1

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