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

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


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

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

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

Multiply (-2 + x) * (-5 + x)
(-2(-5 + x) + x(-5 + x)) = (x + -1)(x + -3)
((-5 * -2 + x * -2) + x(-5 + x)) = (x + -1)(x + -3)
((10 + -2x) + x(-5 + x)) = (x + -1)(x + -3)
(10 + -2x + (-5 * x + x * x)) = (x + -1)(x + -3)
(10 + -2x + (-5x + x2)) = (x + -1)(x + -3)

Combine like terms: -2x + -5x = -7x
(10 + -7x + x2) = (x + -1)(x + -3)

Reorder the terms:
10 + -7x + x2 = (-1 + x)(x + -3)

Reorder the terms:
10 + -7x + x2 = (-1 + x)(-3 + x)

Multiply (-1 + x) * (-3 + x)
10 + -7x + x2 = (-1(-3 + x) + x(-3 + x))
10 + -7x + x2 = ((-3 * -1 + x * -1) + x(-3 + x))
10 + -7x + x2 = ((3 + -1x) + x(-3 + x))
10 + -7x + x2 = (3 + -1x + (-3 * x + x * x))
10 + -7x + x2 = (3 + -1x + (-3x + x2))

Combine like terms: -1x + -3x = -4x
10 + -7x + x2 = (3 + -4x + x2)

Add '-1x2' to each side of the equation.
10 + -7x + x2 + -1x2 = 3 + -4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + -7x + 0 = 3 + -4x + x2 + -1x2
10 + -7x = 3 + -4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + -7x = 3 + -4x + 0
10 + -7x = 3 + -4x

Solving
10 + -7x = 3 + -4x

Solving for variable 'x'.

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

Add '4x' to each side of the equation.
10 + -7x + 4x = 3 + -4x + 4x

Combine like terms: -7x + 4x = -3x
10 + -3x = 3 + -4x + 4x

Combine like terms: -4x + 4x = 0
10 + -3x = 3 + 0
10 + -3x = 3

Add '-10' to each side of the equation.
10 + -10 + -3x = 3 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 3 + -10
-3x = 3 + -10

Combine like terms: 3 + -10 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333

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