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

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


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

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

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

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

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

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

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

Multiply (-2 + x) * (4 + x)
3 + -4x + x2 = (-2(4 + x) + x(4 + x))
3 + -4x + x2 = ((4 * -2 + x * -2) + x(4 + x))
3 + -4x + x2 = ((-8 + -2x) + x(4 + x))
3 + -4x + x2 = (-8 + -2x + (4 * x + x * x))
3 + -4x + x2 = (-8 + -2x + (4x + x2))

Combine like terms: -2x + 4x = 2x
3 + -4x + x2 = (-8 + 2x + x2)

Add '-1x2' to each side of the equation.
3 + -4x + x2 + -1x2 = -8 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -4x + 0 = -8 + 2x + x2 + -1x2
3 + -4x = -8 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -4x = -8 + 2x + 0
3 + -4x = -8 + 2x

Solving
3 + -4x = -8 + 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
3 + -4x + -2x = -8 + 2x + -2x

Combine like terms: -4x + -2x = -6x
3 + -6x = -8 + 2x + -2x

Combine like terms: 2x + -2x = 0
3 + -6x = -8 + 0
3 + -6x = -8

Add '-3' to each side of the equation.
3 + -3 + -6x = -8 + -3

Combine like terms: 3 + -3 = 0
0 + -6x = -8 + -3
-6x = -8 + -3

Combine like terms: -8 + -3 = -11
-6x = -11

Divide each side by '-6'.
x = 1.833333333

Simplifying
x = 1.833333333

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