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

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


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

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

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

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

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

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

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

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

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

Add '-1x2' to each side of the equation.
12 + -7x + x2 + -1x2 = 5 + -6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -7x + 0 = 5 + -6x + x2 + -1x2
12 + -7x = 5 + -6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -7x = 5 + -6x + 0
12 + -7x = 5 + -6x

Solving
12 + -7x = 5 + -6x

Solving for variable 'x'.

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

Add '6x' to each side of the equation.
12 + -7x + 6x = 5 + -6x + 6x

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

Combine like terms: -6x + 6x = 0
12 + -1x = 5 + 0
12 + -1x = 5

Add '-12' to each side of the equation.
12 + -12 + -1x = 5 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 5 + -12
-1x = 5 + -12

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

Divide each side by '-1'.
x = 7

Simplifying
x = 7

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