(x-1)(x-2)-(4x-1)(3x+5)-6=8x-11(x-3)(x+7)

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Solution for (x-1)(x-2)-(4x-1)(3x+5)-6=8x-11(x-3)(x+7) equation: 


Simplifying
(x + -1)(x + -2) + -1(4x + -1)(3x + 5) + -6 = 8x + -11(x + -3)(x + 7)

Reorder the terms:
(-1 + x)(x + -2) + -1(4x + -1)(3x + 5) + -6 = 8x + -11(x + -3)(x + 7)

Reorder the terms:
(-1 + x)(-2 + x) + -1(4x + -1)(3x + 5) + -6 = 8x + -11(x + -3)(x + 7)

Multiply (-1 + x) * (-2 + x)
(-1(-2 + x) + x(-2 + x)) + -1(4x + -1)(3x + 5) + -6 = 8x + -11(x + -3)(x + 7)
((-2 * -1 + x * -1) + x(-2 + x)) + -1(4x + -1)(3x + 5) + -6 = 8x + -11(x + -3)(x + 7)
((2 + -1x) + x(-2 + x)) + -1(4x + -1)(3x + 5) + -6 = 8x + -11(x + -3)(x + 7)
(2 + -1x + (-2 * x + x * x)) + -1(4x + -1)(3x + 5) + -6 = 8x + -11(x + -3)(x + 7)
(2 + -1x + (-2x + x2)) + -1(4x + -1)(3x + 5) + -6 = 8x + -11(x + -3)(x + 7)

Combine like terms: -1x + -2x = -3x
(2 + -3x + x2) + -1(4x + -1)(3x + 5) + -6 = 8x + -11(x + -3)(x + 7)

Reorder the terms:
2 + -3x + x2 + -1(-1 + 4x)(3x + 5) + -6 = 8x + -11(x + -3)(x + 7)

Reorder the terms:
2 + -3x + x2 + -1(-1 + 4x)(5 + 3x) + -6 = 8x + -11(x + -3)(x + 7)

Multiply (-1 + 4x) * (5 + 3x)
2 + -3x + x2 + -1(-1(5 + 3x) + 4x * (5 + 3x)) + -6 = 8x + -11(x + -3)(x + 7)
2 + -3x + x2 + -1((5 * -1 + 3x * -1) + 4x * (5 + 3x)) + -6 = 8x + -11(x + -3)(x + 7)
2 + -3x + x2 + -1((-5 + -3x) + 4x * (5 + 3x)) + -6 = 8x + -11(x + -3)(x + 7)
2 + -3x + x2 + -1(-5 + -3x + (5 * 4x + 3x * 4x)) + -6 = 8x + -11(x + -3)(x + 7)
2 + -3x + x2 + -1(-5 + -3x + (20x + 12x2)) + -6 = 8x + -11(x + -3)(x + 7)

Combine like terms: -3x + 20x = 17x
2 + -3x + x2 + -1(-5 + 17x + 12x2) + -6 = 8x + -11(x + -3)(x + 7)
2 + -3x + x2 + (-5 * -1 + 17x * -1 + 12x2 * -1) + -6 = 8x + -11(x + -3)(x + 7)
2 + -3x + x2 + (5 + -17x + -12x2) + -6 = 8x + -11(x + -3)(x + 7)

Reorder the terms:
2 + 5 + -6 + -3x + -17x + x2 + -12x2 = 8x + -11(x + -3)(x + 7)

Combine like terms: 2 + 5 = 7
7 + -6 + -3x + -17x + x2 + -12x2 = 8x + -11(x + -3)(x + 7)

Combine like terms: 7 + -6 = 1
1 + -3x + -17x + x2 + -12x2 = 8x + -11(x + -3)(x + 7)

Combine like terms: -3x + -17x = -20x
1 + -20x + x2 + -12x2 = 8x + -11(x + -3)(x + 7)

Combine like terms: x2 + -12x2 = -11x2
1 + -20x + -11x2 = 8x + -11(x + -3)(x + 7)

Reorder the terms:
1 + -20x + -11x2 = 8x + -11(-3 + x)(x + 7)

Reorder the terms:
1 + -20x + -11x2 = 8x + -11(-3 + x)(7 + x)

Multiply (-3 + x) * (7 + x)
1 + -20x + -11x2 = 8x + -11(-3(7 + x) + x(7 + x))
1 + -20x + -11x2 = 8x + -11((7 * -3 + x * -3) + x(7 + x))
1 + -20x + -11x2 = 8x + -11((-21 + -3x) + x(7 + x))
1 + -20x + -11x2 = 8x + -11(-21 + -3x + (7 * x + x * x))
1 + -20x + -11x2 = 8x + -11(-21 + -3x + (7x + x2))

Combine like terms: -3x + 7x = 4x
1 + -20x + -11x2 = 8x + -11(-21 + 4x + x2)
1 + -20x + -11x2 = 8x + (-21 * -11 + 4x * -11 + x2 * -11)
1 + -20x + -11x2 = 8x + (231 + -44x + -11x2)

Reorder the terms:
1 + -20x + -11x2 = 231 + 8x + -44x + -11x2

Combine like terms: 8x + -44x = -36x
1 + -20x + -11x2 = 231 + -36x + -11x2

Add '11x2' to each side of the equation.
1 + -20x + -11x2 + 11x2 = 231 + -36x + -11x2 + 11x2

Combine like terms: -11x2 + 11x2 = 0
1 + -20x + 0 = 231 + -36x + -11x2 + 11x2
1 + -20x = 231 + -36x + -11x2 + 11x2

Combine like terms: -11x2 + 11x2 = 0
1 + -20x = 231 + -36x + 0
1 + -20x = 231 + -36x

Solving
1 + -20x = 231 + -36x

Solving for variable 'x'.

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

Add '36x' to each side of the equation.
1 + -20x + 36x = 231 + -36x + 36x

Combine like terms: -20x + 36x = 16x
1 + 16x = 231 + -36x + 36x

Combine like terms: -36x + 36x = 0
1 + 16x = 231 + 0
1 + 16x = 231

Add '-1' to each side of the equation.
1 + -1 + 16x = 231 + -1

Combine like terms: 1 + -1 = 0
0 + 16x = 231 + -1
16x = 231 + -1

Combine like terms: 231 + -1 = 230
16x = 230

Divide each side by '16'.
x = 14.375

Simplifying
x = 14.375

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