(x-2)(x-4)=(x-3)(x+6)

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Solution for (x-2)(x-4)=(x-3)(x+6) equation: 


Simplifying
(x + -2)(x + -4) = (x + -3)(x + 6)

Reorder the terms:
(-2 + x)(x + -4) = (x + -3)(x + 6)

Reorder the terms:
(-2 + x)(-4 + x) = (x + -3)(x + 6)

Multiply (-2 + x) * (-4 + x)
(-2(-4 + x) + x(-4 + x)) = (x + -3)(x + 6)
((-4 * -2 + x * -2) + x(-4 + x)) = (x + -3)(x + 6)
((8 + -2x) + x(-4 + x)) = (x + -3)(x + 6)
(8 + -2x + (-4 * x + x * x)) = (x + -3)(x + 6)
(8 + -2x + (-4x + x2)) = (x + -3)(x + 6)

Combine like terms: -2x + -4x = -6x
(8 + -6x + x2) = (x + -3)(x + 6)

Reorder the terms:
8 + -6x + x2 = (-3 + x)(x + 6)

Reorder the terms:
8 + -6x + x2 = (-3 + x)(6 + x)

Multiply (-3 + x) * (6 + x)
8 + -6x + x2 = (-3(6 + x) + x(6 + x))
8 + -6x + x2 = ((6 * -3 + x * -3) + x(6 + x))
8 + -6x + x2 = ((-18 + -3x) + x(6 + x))
8 + -6x + x2 = (-18 + -3x + (6 * x + x * x))
8 + -6x + x2 = (-18 + -3x + (6x + x2))

Combine like terms: -3x + 6x = 3x
8 + -6x + x2 = (-18 + 3x + x2)

Add '-1x2' to each side of the equation.
8 + -6x + x2 + -1x2 = -18 + 3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + -6x + 0 = -18 + 3x + x2 + -1x2
8 + -6x = -18 + 3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + -6x = -18 + 3x + 0
8 + -6x = -18 + 3x

Solving
8 + -6x = -18 + 3x

Solving for variable 'x'.

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

Add '-3x' to each side of the equation.
8 + -6x + -3x = -18 + 3x + -3x

Combine like terms: -6x + -3x = -9x
8 + -9x = -18 + 3x + -3x

Combine like terms: 3x + -3x = 0
8 + -9x = -18 + 0
8 + -9x = -18

Add '-8' to each side of the equation.
8 + -8 + -9x = -18 + -8

Combine like terms: 8 + -8 = 0
0 + -9x = -18 + -8
-9x = -18 + -8

Combine like terms: -18 + -8 = -26
-9x = -26

Divide each side by '-9'.
x = 2.888888889

Simplifying
x = 2.888888889

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