(x-2)(x-3)-(x-1)(x-4)=0

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Solution for (x-2)(x-3)-(x-1)(x-4)=0 equation: 


Simplifying
(x + -2)(x + -3) + -1(x + -1)(x + -4) = 0

Reorder the terms:
(-2 + x)(x + -3) + -1(x + -1)(x + -4) = 0

Reorder the terms:
(-2 + x)(-3 + x) + -1(x + -1)(x + -4) = 0

Multiply (-2 + x) * (-3 + x)
(-2(-3 + x) + x(-3 + x)) + -1(x + -1)(x + -4) = 0
((-3 * -2 + x * -2) + x(-3 + x)) + -1(x + -1)(x + -4) = 0
((6 + -2x) + x(-3 + x)) + -1(x + -1)(x + -4) = 0
(6 + -2x + (-3 * x + x * x)) + -1(x + -1)(x + -4) = 0
(6 + -2x + (-3x + x2)) + -1(x + -1)(x + -4) = 0

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2) + -1(x + -1)(x + -4) = 0

Reorder the terms:
6 + -5x + x2 + -1(-1 + x)(x + -4) = 0

Reorder the terms:
6 + -5x + x2 + -1(-1 + x)(-4 + x) = 0

Multiply (-1 + x) * (-4 + x)
6 + -5x + x2 + -1(-1(-4 + x) + x(-4 + x)) = 0
6 + -5x + x2 + -1((-4 * -1 + x * -1) + x(-4 + x)) = 0
6 + -5x + x2 + -1((4 + -1x) + x(-4 + x)) = 0
6 + -5x + x2 + -1(4 + -1x + (-4 * x + x * x)) = 0
6 + -5x + x2 + -1(4 + -1x + (-4x + x2)) = 0

Combine like terms: -1x + -4x = -5x
6 + -5x + x2 + -1(4 + -5x + x2) = 0
6 + -5x + x2 + (4 * -1 + -5x * -1 + x2 * -1) = 0
6 + -5x + x2 + (-4 + 5x + -1x2) = 0

Reorder the terms:
6 + -4 + -5x + 5x + x2 + -1x2 = 0

Combine like terms: 6 + -4 = 2
2 + -5x + 5x + x2 + -1x2 = 0

Combine like terms: -5x + 5x = 0
2 + 0 + x2 + -1x2 = 0
2 + x2 + -1x2 = 0

Combine like terms: x2 + -1x2 = 0
2 + 0 = 0
2 = 0

Solving
2 = 0

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

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