(2x-3)(x-5)=(x-6)(x-3)-3(X-1)

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Solution for (2x-3)(x-5)=(x-6)(x-3)-3(X-1) equation:


Simplifying
(2x + -3)(x + -5) = (x + -6)(x + -3) + -3(X + -1)

Reorder the terms:
(-3 + 2x)(x + -5) = (x + -6)(x + -3) + -3(X + -1)

Reorder the terms:
(-3 + 2x)(-5 + x) = (x + -6)(x + -3) + -3(X + -1)

Multiply (-3 + 2x) * (-5 + x)
(-3(-5 + x) + 2x * (-5 + x)) = (x + -6)(x + -3) + -3(X + -1)
((-5 * -3 + x * -3) + 2x * (-5 + x)) = (x + -6)(x + -3) + -3(X + -1)
((15 + -3x) + 2x * (-5 + x)) = (x + -6)(x + -3) + -3(X + -1)
(15 + -3x + (-5 * 2x + x * 2x)) = (x + -6)(x + -3) + -3(X + -1)
(15 + -3x + (-10x + 2x2)) = (x + -6)(x + -3) + -3(X + -1)

Combine like terms: -3x + -10x = -13x
(15 + -13x + 2x2) = (x + -6)(x + -3) + -3(X + -1)

Reorder the terms:
15 + -13x + 2x2 = (-6 + x)(x + -3) + -3(X + -1)

Reorder the terms:
15 + -13x + 2x2 = (-6 + x)(-3 + x) + -3(X + -1)

Multiply (-6 + x) * (-3 + x)
15 + -13x + 2x2 = (-6(-3 + x) + x(-3 + x)) + -3(X + -1)
15 + -13x + 2x2 = ((-3 * -6 + x * -6) + x(-3 + x)) + -3(X + -1)
15 + -13x + 2x2 = ((18 + -6x) + x(-3 + x)) + -3(X + -1)
15 + -13x + 2x2 = (18 + -6x + (-3 * x + x * x)) + -3(X + -1)
15 + -13x + 2x2 = (18 + -6x + (-3x + x2)) + -3(X + -1)

Combine like terms: -6x + -3x = -9x
15 + -13x + 2x2 = (18 + -9x + x2) + -3(X + -1)

Reorder the terms:
15 + -13x + 2x2 = 18 + -9x + x2 + -3(-1 + X)
15 + -13x + 2x2 = 18 + -9x + x2 + (-1 * -3 + X * -3)
15 + -13x + 2x2 = 18 + -9x + x2 + (3 + -3X)

Reorder the terms:
15 + -13x + 2x2 = 18 + 3 + -3X + -9x + x2

Combine like terms: 18 + 3 = 21
15 + -13x + 2x2 = 21 + -3X + -9x + x2

Solving
15 + -13x + 2x2 = 21 + -3X + -9x + x2

Solving for variable 'x'.

Reorder the terms:
15 + -21 + 3X + -13x + 9x + 2x2 + -1x2 = 21 + -3X + -9x + x2 + -21 + 3X + 9x + -1x2

Combine like terms: 15 + -21 = -6
-6 + 3X + -13x + 9x + 2x2 + -1x2 = 21 + -3X + -9x + x2 + -21 + 3X + 9x + -1x2

Combine like terms: -13x + 9x = -4x
-6 + 3X + -4x + 2x2 + -1x2 = 21 + -3X + -9x + x2 + -21 + 3X + 9x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-6 + 3X + -4x + 1x2 = 21 + -3X + -9x + x2 + -21 + 3X + 9x + -1x2

Reorder the terms:
-6 + 3X + -4x + 1x2 = 21 + -21 + -3X + 3X + -9x + 9x + x2 + -1x2

Combine like terms: 21 + -21 = 0
-6 + 3X + -4x + 1x2 = 0 + -3X + 3X + -9x + 9x + x2 + -1x2
-6 + 3X + -4x + 1x2 = -3X + 3X + -9x + 9x + x2 + -1x2

Combine like terms: -3X + 3X = 0
-6 + 3X + -4x + 1x2 = 0 + -9x + 9x + x2 + -1x2
-6 + 3X + -4x + 1x2 = -9x + 9x + x2 + -1x2

Combine like terms: -9x + 9x = 0
-6 + 3X + -4x + 1x2 = 0 + x2 + -1x2
-6 + 3X + -4x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + 3X + -4x + 1x2 = 0

The solution to this equation could not be determined.

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