(x-4)(x-3)-(x-5)(x-1)=x+2

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Solution for (x-4)(x-3)-(x-5)(x-1)=x+2 equation: 


Simplifying
(x + -4)(x + -3) + -1(x + -5)(x + -1) = x + 2

Reorder the terms:
(-4 + x)(x + -3) + -1(x + -5)(x + -1) = x + 2

Reorder the terms:
(-4 + x)(-3 + x) + -1(x + -5)(x + -1) = x + 2

Multiply (-4 + x) * (-3 + x)
(-4(-3 + x) + x(-3 + x)) + -1(x + -5)(x + -1) = x + 2
((-3 * -4 + x * -4) + x(-3 + x)) + -1(x + -5)(x + -1) = x + 2
((12 + -4x) + x(-3 + x)) + -1(x + -5)(x + -1) = x + 2
(12 + -4x + (-3 * x + x * x)) + -1(x + -5)(x + -1) = x + 2
(12 + -4x + (-3x + x2)) + -1(x + -5)(x + -1) = x + 2

Combine like terms: -4x + -3x = -7x
(12 + -7x + x2) + -1(x + -5)(x + -1) = x + 2

Reorder the terms:
12 + -7x + x2 + -1(-5 + x)(x + -1) = x + 2

Reorder the terms:
12 + -7x + x2 + -1(-5 + x)(-1 + x) = x + 2

Multiply (-5 + x) * (-1 + x)
12 + -7x + x2 + -1(-5(-1 + x) + x(-1 + x)) = x + 2
12 + -7x + x2 + -1((-1 * -5 + x * -5) + x(-1 + x)) = x + 2
12 + -7x + x2 + -1((5 + -5x) + x(-1 + x)) = x + 2
12 + -7x + x2 + -1(5 + -5x + (-1 * x + x * x)) = x + 2
12 + -7x + x2 + -1(5 + -5x + (-1x + x2)) = x + 2

Combine like terms: -5x + -1x = -6x
12 + -7x + x2 + -1(5 + -6x + x2) = x + 2
12 + -7x + x2 + (5 * -1 + -6x * -1 + x2 * -1) = x + 2
12 + -7x + x2 + (-5 + 6x + -1x2) = x + 2

Reorder the terms:
12 + -5 + -7x + 6x + x2 + -1x2 = x + 2

Combine like terms: 12 + -5 = 7
7 + -7x + 6x + x2 + -1x2 = x + 2

Combine like terms: -7x + 6x = -1x
7 + -1x + x2 + -1x2 = x + 2

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

Reorder the terms:
7 + -1x = 2 + x

Solving
7 + -1x = 2 + x

Solving for variable 'x'.

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

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

Combine like terms: -1x + -1x = -2x
7 + -2x = 2 + x + -1x

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

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

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

Combine like terms: 2 + -7 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

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