(x+1)(x+2)(x+3)(x+4)(x+5)(x+6)=720

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Solution for (x+1)(x+2)(x+3)(x+4)(x+5)(x+6)=720 equation:


Simplifying
(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6) = 720

Reorder the terms:
(1 + x)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6) = 720

Reorder the terms:
(1 + x)(2 + x)(x + 3)(x + 4)(x + 5)(x + 6) = 720

Reorder the terms:
(1 + x)(2 + x)(3 + x)(x + 4)(x + 5)(x + 6) = 720

Reorder the terms:
(1 + x)(2 + x)(3 + x)(4 + x)(x + 5)(x + 6) = 720

Reorder the terms:
(1 + x)(2 + x)(3 + x)(4 + x)(5 + x)(x + 6) = 720

Reorder the terms:
(1 + x)(2 + x)(3 + x)(4 + x)(5 + x)(6 + x) = 720

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x))(3 + x)(4 + x)(5 + x)(6 + x) = 720
((2 * 1 + x * 1) + x(2 + x))(3 + x)(4 + x)(5 + x)(6 + x) = 720
((2 + 1x) + x(2 + x))(3 + x)(4 + x)(5 + x)(6 + x) = 720
(2 + 1x + (2 * x + x * x))(3 + x)(4 + x)(5 + x)(6 + x) = 720
(2 + 1x + (2x + x2))(3 + x)(4 + x)(5 + x)(6 + x) = 720

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2)(3 + x)(4 + x)(5 + x)(6 + x) = 720

Multiply (2 + 3x + x2) * (3 + x)
(2(3 + x) + 3x * (3 + x) + x2(3 + x))(4 + x)(5 + x)(6 + x) = 720
((3 * 2 + x * 2) + 3x * (3 + x) + x2(3 + x))(4 + x)(5 + x)(6 + x) = 720
((6 + 2x) + 3x * (3 + x) + x2(3 + x))(4 + x)(5 + x)(6 + x) = 720
(6 + 2x + (3 * 3x + x * 3x) + x2(3 + x))(4 + x)(5 + x)(6 + x) = 720
(6 + 2x + (9x + 3x2) + x2(3 + x))(4 + x)(5 + x)(6 + x) = 720
(6 + 2x + 9x + 3x2 + (3 * x2 + x * x2))(4 + x)(5 + x)(6 + x) = 720
(6 + 2x + 9x + 3x2 + (3x2 + x3))(4 + x)(5 + x)(6 + x) = 720

Combine like terms: 2x + 9x = 11x
(6 + 11x + 3x2 + 3x2 + x3)(4 + x)(5 + x)(6 + x) = 720

Combine like terms: 3x2 + 3x2 = 6x2
(6 + 11x + 6x2 + x3)(4 + x)(5 + x)(6 + x) = 720

Multiply (6 + 11x + 6x2 + x3) * (4 + x)
(6(4 + x) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x))(5 + x)(6 + x) = 720
((4 * 6 + x * 6) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x))(5 + x)(6 + x) = 720
((24 + 6x) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x))(5 + x)(6 + x) = 720
(24 + 6x + (4 * 11x + x * 11x) + 6x2 * (4 + x) + x3(4 + x))(5 + x)(6 + x) = 720
(24 + 6x + (44x + 11x2) + 6x2 * (4 + x) + x3(4 + x))(5 + x)(6 + x) = 720
(24 + 6x + 44x + 11x2 + (4 * 6x2 + x * 6x2) + x3(4 + x))(5 + x)(6 + x) = 720
(24 + 6x + 44x + 11x2 + (24x2 + 6x3) + x3(4 + x))(5 + x)(6 + x) = 720
(24 + 6x + 44x + 11x2 + 24x2 + 6x3 + (4 * x3 + x * x3))(5 + x)(6 + x) = 720
(24 + 6x + 44x + 11x2 + 24x2 + 6x3 + (4x3 + x4))(5 + x)(6 + x) = 720

Combine like terms: 6x + 44x = 50x
(24 + 50x + 11x2 + 24x2 + 6x3 + 4x3 + x4)(5 + x)(6 + x) = 720

Combine like terms: 11x2 + 24x2 = 35x2
(24 + 50x + 35x2 + 6x3 + 4x3 + x4)(5 + x)(6 + x) = 720

Combine like terms: 6x3 + 4x3 = 10x3
(24 + 50x + 35x2 + 10x3 + x4)(5 + x)(6 + x) = 720

Multiply (24 + 50x + 35x2 + 10x3 + x4) * (5 + x)
(24(5 + x) + 50x * (5 + x) + 35x2 * (5 + x) + 10x3 * (5 + x) + x4(5 + x))(6 + x) = 720
((5 * 24 + x * 24) + 50x * (5 + x) + 35x2 * (5 + x) + 10x3 * (5 + x) + x4(5 + x))(6 + x) = 720
((120 + 24x) + 50x * (5 + x) + 35x2 * (5 + x) + 10x3 * (5 + x) + x4(5 + x))(6 + x) = 720
(120 + 24x + (5 * 50x + x * 50x) + 35x2 * (5 + x) + 10x3 * (5 + x) + x4(5 + x))(6 + x) = 720
(120 + 24x + (250x + 50x2) + 35x2 * (5 + x) + 10x3 * (5 + x) + x4(5 + x))(6 + x) = 720
(120 + 24x + 250x + 50x2 + (5 * 35x2 + x * 35x2) + 10x3 * (5 + x) + x4(5 + x))(6 + x) = 720
(120 + 24x + 250x + 50x2 + (175x2 + 35x3) + 10x3 * (5 + x) + x4(5 + x))(6 + x) = 720
(120 + 24x + 250x + 50x2 + 175x2 + 35x3 + (5 * 10x3 + x * 10x3) + x4(5 + x))(6 + x) = 720
(120 + 24x + 250x + 50x2 + 175x2 + 35x3 + (50x3 + 10x4) + x4(5 + x))(6 + x) = 720
(120 + 24x + 250x + 50x2 + 175x2 + 35x3 + 50x3 + 10x4 + (5 * x4 + x * x4))(6 + x) = 720
(120 + 24x + 250x + 50x2 + 175x2 + 35x3 + 50x3 + 10x4 + (5x4 + x5))(6 + x) = 720

Combine like terms: 24x + 250x = 274x
(120 + 274x + 50x2 + 175x2 + 35x3 + 50x3 + 10x4 + 5x4 + x5)(6 + x) = 720

Combine like terms: 50x2 + 175x2 = 225x2
(120 + 274x + 225x2 + 35x3 + 50x3 + 10x4 + 5x4 + x5)(6 + x) = 720

Combine like terms: 35x3 + 50x3 = 85x3
(120 + 274x + 225x2 + 85x3 + 10x4 + 5x4 + x5)(6 + x) = 720

Combine like terms: 10x4 + 5x4 = 15x4
(120 + 274x + 225x2 + 85x3 + 15x4 + x5)(6 + x) = 720

Multiply (120 + 274x + 225x2 + 85x3 + 15x4 + x5) * (6 + x)
(120(6 + x) + 274x * (6 + x) + 225x2 * (6 + x) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x)) = 720
((6 * 120 + x * 120) + 274x * (6 + x) + 225x2 * (6 + x) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x)) = 720
((720 + 120x) + 274x * (6 + x) + 225x2 * (6 + x) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x)) = 720
(720 + 120x + (6 * 274x + x * 274x) + 225x2 * (6 + x) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x)) = 720
(720 + 120x + (1644x + 274x2) + 225x2 * (6 + x) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x)) = 720
(720 + 120x + 1644x + 274x2 + (6 * 225x2 + x * 225x2) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x)) = 720
(720 + 120x + 1644x + 274x2 + (1350x2 + 225x3) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x)) = 720
(720 + 120x + 1644x + 274x2 + 1350x2 + 225x3 + (6 * 85x3 + x * 85x3) + 15x4 * (6 + x) + x5(6 + x)) = 720
(720 + 120x + 1644x + 274x2 + 1350x2 + 225x3 + (510x3 + 85x4) + 15x4 * (6 + x) + x5(6 + x)) = 720
(720 + 120x + 1644x + 274x2 + 1350x2 + 225x3 + 510x3 + 85x4 + (6 * 15x4 + x * 15x4) + x5(6 + x)) = 720
(720 + 120x + 1644x + 274x2 + 1350x2 + 225x3 + 510x3 + 85x4 + (90x4 + 15x5) + x5(6 + x)) = 720
(720 + 120x + 1644x + 274x2 + 1350x2 + 225x3 + 510x3 + 85x4 + 90x4 + 15x5 + (6 * x5 + x * x5)) = 720
(720 + 120x + 1644x + 274x2 + 1350x2 + 225x3 + 510x3 + 85x4 + 90x4 + 15x5 + (6x5 + x6)) = 720

Combine like terms: 120x + 1644x = 1764x
(720 + 1764x + 274x2 + 1350x2 + 225x3 + 510x3 + 85x4 + 90x4 + 15x5 + 6x5 + x6) = 720

Combine like terms: 274x2 + 1350x2 = 1624x2
(720 + 1764x + 1624x2 + 225x3 + 510x3 + 85x4 + 90x4 + 15x5 + 6x5 + x6) = 720

Combine like terms: 225x3 + 510x3 = 735x3
(720 + 1764x + 1624x2 + 735x3 + 85x4 + 90x4 + 15x5 + 6x5 + x6) = 720

Combine like terms: 85x4 + 90x4 = 175x4
(720 + 1764x + 1624x2 + 735x3 + 175x4 + 15x5 + 6x5 + x6) = 720

Combine like terms: 15x5 + 6x5 = 21x5
(720 + 1764x + 1624x2 + 735x3 + 175x4 + 21x5 + x6) = 720

Add '-720' to each side of the equation.
720 + 1764x + 1624x2 + 735x3 + 175x4 + 21x5 + -720 + x6 = 720 + -720

Reorder the terms:
720 + -720 + 1764x + 1624x2 + 735x3 + 175x4 + 21x5 + x6 = 720 + -720

Combine like terms: 720 + -720 = 0
0 + 1764x + 1624x2 + 735x3 + 175x4 + 21x5 + x6 = 720 + -720
1764x + 1624x2 + 735x3 + 175x4 + 21x5 + x6 = 720 + -720

Combine like terms: 720 + -720 = 0
1764x + 1624x2 + 735x3 + 175x4 + 21x5 + x6 = 0

Solving
1764x + 1624x2 + 735x3 + 175x4 + 21x5 + x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1764 + 1624x + 735x2 + 175x3 + 21x4 + x5) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(1764 + 1624x + 735x2 + 175x3 + 21x4 + x5)' equal to zero and attempt to solve: Simplifying 1764 + 1624x + 735x2 + 175x3 + 21x4 + x5 = 0 Solving 1764 + 1624x + 735x2 + 175x3 + 21x4 + x5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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