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

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


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

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

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

Multiply (-2 + x) * (4 + x)
(-2(4 + x) + x(4 + x)) + -1(x + -3)(x + -1) = 0
((4 * -2 + x * -2) + x(4 + x)) + -1(x + -3)(x + -1) = 0
((-8 + -2x) + x(4 + x)) + -1(x + -3)(x + -1) = 0
(-8 + -2x + (4 * x + x * x)) + -1(x + -3)(x + -1) = 0
(-8 + -2x + (4x + x2)) + -1(x + -3)(x + -1) = 0

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

Reorder the terms:
-8 + 2x + x2 + -1(-3 + x)(x + -1) = 0

Reorder the terms:
-8 + 2x + x2 + -1(-3 + x)(-1 + x) = 0

Multiply (-3 + x) * (-1 + x)
-8 + 2x + x2 + -1(-3(-1 + x) + x(-1 + x)) = 0
-8 + 2x + x2 + -1((-1 * -3 + x * -3) + x(-1 + x)) = 0
-8 + 2x + x2 + -1((3 + -3x) + x(-1 + x)) = 0
-8 + 2x + x2 + -1(3 + -3x + (-1 * x + x * x)) = 0
-8 + 2x + x2 + -1(3 + -3x + (-1x + x2)) = 0

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

Reorder the terms:
-8 + -3 + 2x + 4x + x2 + -1x2 = 0

Combine like terms: -8 + -3 = -11
-11 + 2x + 4x + x2 + -1x2 = 0

Combine like terms: 2x + 4x = 6x
-11 + 6x + x2 + -1x2 = 0

Combine like terms: x2 + -1x2 = 0
-11 + 6x + 0 = 0
-11 + 6x = 0

Solving
-11 + 6x = 0

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + 6x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 6x = 0 + 11
6x = 0 + 11

Combine like terms: 0 + 11 = 11
6x = 11

Divide each side by '6'.
x = 1.833333333

Simplifying
x = 1.833333333

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