(x-1)(x-2)=(x-3)(x-4)

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Solution for (x-1)(x-2)=(x-3)(x-4) equation: 


Simplifying
(x + -1)(x + -2) = (x + -3)(x + -4)

Reorder the terms:
(-1 + x)(x + -2) = (x + -3)(x + -4)

Reorder the terms:
(-1 + x)(-2 + x) = (x + -3)(x + -4)

Multiply (-1 + x) * (-2 + x)
(-1(-2 + x) + x(-2 + x)) = (x + -3)(x + -4)
((-2 * -1 + x * -1) + x(-2 + x)) = (x + -3)(x + -4)
((2 + -1x) + x(-2 + x)) = (x + -3)(x + -4)
(2 + -1x + (-2 * x + x * x)) = (x + -3)(x + -4)
(2 + -1x + (-2x + x2)) = (x + -3)(x + -4)

Combine like terms: -1x + -2x = -3x
(2 + -3x + x2) = (x + -3)(x + -4)

Reorder the terms:
2 + -3x + x2 = (-3 + x)(x + -4)

Reorder the terms:
2 + -3x + x2 = (-3 + x)(-4 + x)

Multiply (-3 + x) * (-4 + x)
2 + -3x + x2 = (-3(-4 + x) + x(-4 + x))
2 + -3x + x2 = ((-4 * -3 + x * -3) + x(-4 + x))
2 + -3x + x2 = ((12 + -3x) + x(-4 + x))
2 + -3x + x2 = (12 + -3x + (-4 * x + x * x))
2 + -3x + x2 = (12 + -3x + (-4x + x2))

Combine like terms: -3x + -4x = -7x
2 + -3x + x2 = (12 + -7x + x2)

Add '-1x2' to each side of the equation.
2 + -3x + x2 + -1x2 = 12 + -7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -3x + 0 = 12 + -7x + x2 + -1x2
2 + -3x = 12 + -7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -3x = 12 + -7x + 0
2 + -3x = 12 + -7x

Solving
2 + -3x = 12 + -7x

Solving for variable 'x'.

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

Add '7x' to each side of the equation.
2 + -3x + 7x = 12 + -7x + 7x

Combine like terms: -3x + 7x = 4x
2 + 4x = 12 + -7x + 7x

Combine like terms: -7x + 7x = 0
2 + 4x = 12 + 0
2 + 4x = 12

Add '-2' to each side of the equation.
2 + -2 + 4x = 12 + -2

Combine like terms: 2 + -2 = 0
0 + 4x = 12 + -2
4x = 12 + -2

Combine like terms: 12 + -2 = 10
4x = 10

Divide each side by '4'.
x = 2.5

Simplifying
x = 2.5

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