x((3x-3)(2x-8)+(2x+2)(3x+1))=(5x-5)(3x+1)(2x-8)

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Solution for x((3x-3)(2x-8)+(2x+2)(3x+1))=(5x-5)(3x+1)(2x-8) equation:


Simplifying
x((3x + -3)(2x + -8) + (2x + 2)(3x + 1)) = (5x + -5)(3x + 1)(2x + -8)

Reorder the terms:
x((-3 + 3x)(2x + -8) + (2x + 2)(3x + 1)) = (5x + -5)(3x + 1)(2x + -8)

Reorder the terms:
x((-3 + 3x)(-8 + 2x) + (2x + 2)(3x + 1)) = (5x + -5)(3x + 1)(2x + -8)

Multiply (-3 + 3x) * (-8 + 2x)
x((-3(-8 + 2x) + 3x * (-8 + 2x)) + (2x + 2)(3x + 1)) = (5x + -5)(3x + 1)(2x + -8)
x(((-8 * -3 + 2x * -3) + 3x * (-8 + 2x)) + (2x + 2)(3x + 1)) = (5x + -5)(3x + 1)(2x + -8)
x(((24 + -6x) + 3x * (-8 + 2x)) + (2x + 2)(3x + 1)) = (5x + -5)(3x + 1)(2x + -8)
x((24 + -6x + (-8 * 3x + 2x * 3x)) + (2x + 2)(3x + 1)) = (5x + -5)(3x + 1)(2x + -8)
x((24 + -6x + (-24x + 6x2)) + (2x + 2)(3x + 1)) = (5x + -5)(3x + 1)(2x + -8)

Combine like terms: -6x + -24x = -30x
x((24 + -30x + 6x2) + (2x + 2)(3x + 1)) = (5x + -5)(3x + 1)(2x + -8)

Reorder the terms:
x(24 + -30x + 6x2 + (2 + 2x)(3x + 1)) = (5x + -5)(3x + 1)(2x + -8)

Reorder the terms:
x(24 + -30x + 6x2 + (2 + 2x)(1 + 3x)) = (5x + -5)(3x + 1)(2x + -8)

Multiply (2 + 2x) * (1 + 3x)
x(24 + -30x + 6x2 + (2(1 + 3x) + 2x * (1 + 3x))) = (5x + -5)(3x + 1)(2x + -8)
x(24 + -30x + 6x2 + ((1 * 2 + 3x * 2) + 2x * (1 + 3x))) = (5x + -5)(3x + 1)(2x + -8)
x(24 + -30x + 6x2 + ((2 + 6x) + 2x * (1 + 3x))) = (5x + -5)(3x + 1)(2x + -8)
x(24 + -30x + 6x2 + (2 + 6x + (1 * 2x + 3x * 2x))) = (5x + -5)(3x + 1)(2x + -8)
x(24 + -30x + 6x2 + (2 + 6x + (2x + 6x2))) = (5x + -5)(3x + 1)(2x + -8)

Combine like terms: 6x + 2x = 8x
x(24 + -30x + 6x2 + (2 + 8x + 6x2)) = (5x + -5)(3x + 1)(2x + -8)

Reorder the terms:
x(24 + 2 + -30x + 8x + 6x2 + 6x2) = (5x + -5)(3x + 1)(2x + -8)

Combine like terms: 24 + 2 = 26
x(26 + -30x + 8x + 6x2 + 6x2) = (5x + -5)(3x + 1)(2x + -8)

Combine like terms: -30x + 8x = -22x
x(26 + -22x + 6x2 + 6x2) = (5x + -5)(3x + 1)(2x + -8)

Combine like terms: 6x2 + 6x2 = 12x2
x(26 + -22x + 12x2) = (5x + -5)(3x + 1)(2x + -8)
(26 * x + -22x * x + 12x2 * x) = (5x + -5)(3x + 1)(2x + -8)
(26x + -22x2 + 12x3) = (5x + -5)(3x + 1)(2x + -8)

Reorder the terms:
26x + -22x2 + 12x3 = (-5 + 5x)(3x + 1)(2x + -8)

Reorder the terms:
26x + -22x2 + 12x3 = (-5 + 5x)(1 + 3x)(2x + -8)

Reorder the terms:
26x + -22x2 + 12x3 = (-5 + 5x)(1 + 3x)(-8 + 2x)

Multiply (-5 + 5x) * (1 + 3x)
26x + -22x2 + 12x3 = (-5(1 + 3x) + 5x * (1 + 3x))(-8 + 2x)
26x + -22x2 + 12x3 = ((1 * -5 + 3x * -5) + 5x * (1 + 3x))(-8 + 2x)
26x + -22x2 + 12x3 = ((-5 + -15x) + 5x * (1 + 3x))(-8 + 2x)
26x + -22x2 + 12x3 = (-5 + -15x + (1 * 5x + 3x * 5x))(-8 + 2x)
26x + -22x2 + 12x3 = (-5 + -15x + (5x + 15x2))(-8 + 2x)

Combine like terms: -15x + 5x = -10x
26x + -22x2 + 12x3 = (-5 + -10x + 15x2)(-8 + 2x)

Multiply (-5 + -10x + 15x2) * (-8 + 2x)
26x + -22x2 + 12x3 = (-5(-8 + 2x) + -10x * (-8 + 2x) + 15x2 * (-8 + 2x))
26x + -22x2 + 12x3 = ((-8 * -5 + 2x * -5) + -10x * (-8 + 2x) + 15x2 * (-8 + 2x))
26x + -22x2 + 12x3 = ((40 + -10x) + -10x * (-8 + 2x) + 15x2 * (-8 + 2x))
26x + -22x2 + 12x3 = (40 + -10x + (-8 * -10x + 2x * -10x) + 15x2 * (-8 + 2x))
26x + -22x2 + 12x3 = (40 + -10x + (80x + -20x2) + 15x2 * (-8 + 2x))
26x + -22x2 + 12x3 = (40 + -10x + 80x + -20x2 + (-8 * 15x2 + 2x * 15x2))
26x + -22x2 + 12x3 = (40 + -10x + 80x + -20x2 + (-120x2 + 30x3))

Combine like terms: -10x + 80x = 70x
26x + -22x2 + 12x3 = (40 + 70x + -20x2 + -120x2 + 30x3)

Combine like terms: -20x2 + -120x2 = -140x2
26x + -22x2 + 12x3 = (40 + 70x + -140x2 + 30x3)

Solving
26x + -22x2 + 12x3 = 40 + 70x + -140x2 + 30x3

Solving for variable 'x'.

Reorder the terms:
-40 + 26x + -70x + -22x2 + 140x2 + 12x3 + -30x3 = 40 + 70x + -140x2 + 30x3 + -40 + -70x + 140x2 + -30x3

Combine like terms: 26x + -70x = -44x
-40 + -44x + -22x2 + 140x2 + 12x3 + -30x3 = 40 + 70x + -140x2 + 30x3 + -40 + -70x + 140x2 + -30x3

Combine like terms: -22x2 + 140x2 = 118x2
-40 + -44x + 118x2 + 12x3 + -30x3 = 40 + 70x + -140x2 + 30x3 + -40 + -70x + 140x2 + -30x3

Combine like terms: 12x3 + -30x3 = -18x3
-40 + -44x + 118x2 + -18x3 = 40 + 70x + -140x2 + 30x3 + -40 + -70x + 140x2 + -30x3

Reorder the terms:
-40 + -44x + 118x2 + -18x3 = 40 + -40 + 70x + -70x + -140x2 + 140x2 + 30x3 + -30x3

Combine like terms: 40 + -40 = 0
-40 + -44x + 118x2 + -18x3 = 0 + 70x + -70x + -140x2 + 140x2 + 30x3 + -30x3
-40 + -44x + 118x2 + -18x3 = 70x + -70x + -140x2 + 140x2 + 30x3 + -30x3

Combine like terms: 70x + -70x = 0
-40 + -44x + 118x2 + -18x3 = 0 + -140x2 + 140x2 + 30x3 + -30x3
-40 + -44x + 118x2 + -18x3 = -140x2 + 140x2 + 30x3 + -30x3

Combine like terms: -140x2 + 140x2 = 0
-40 + -44x + 118x2 + -18x3 = 0 + 30x3 + -30x3
-40 + -44x + 118x2 + -18x3 = 30x3 + -30x3

Combine like terms: 30x3 + -30x3 = 0
-40 + -44x + 118x2 + -18x3 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + -22x + 59x2 + -9x3) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-20 + -22x + 59x2 + -9x3)' equal to zero and attempt to solve: Simplifying -20 + -22x + 59x2 + -9x3 = 0 Solving -20 + -22x + 59x2 + -9x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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