(X+4)(x+5)(x+6)(x+7)=1680

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Solution for (X+4)(x+5)(x+6)(x+7)=1680 equation: 


Simplifying
(X + 4)(x + 5)(x + 6)(x + 7) = 1680

Reorder the terms:
(4 + X)(x + 5)(x + 6)(x + 7) = 1680

Reorder the terms:
(4 + X)(5 + x)(x + 6)(x + 7) = 1680

Reorder the terms:
(4 + X)(5 + x)(6 + x)(x + 7) = 1680

Reorder the terms:
(4 + X)(5 + x)(6 + x)(7 + x) = 1680

Multiply (4 + X) * (5 + x)
(4(5 + x) + X(5 + x))(6 + x)(7 + x) = 1680
((5 * 4 + x * 4) + X(5 + x))(6 + x)(7 + x) = 1680
((20 + 4x) + X(5 + x))(6 + x)(7 + x) = 1680
(20 + 4x + (5 * X + x * X))(6 + x)(7 + x) = 1680
(20 + 4x + (5X + xX))(6 + x)(7 + x) = 1680

Reorder the terms:
(20 + 5X + 4x + xX)(6 + x)(7 + x) = 1680
(20 + 5X + 4x + xX)(6 + x)(7 + x) = 1680

Multiply (20 + 5X + 4x + xX) * (6 + x)
(20(6 + x) + 5X * (6 + x) + 4x * (6 + x) + xX(6 + x))(7 + x) = 1680
((6 * 20 + x * 20) + 5X * (6 + x) + 4x * (6 + x) + xX(6 + x))(7 + x) = 1680
((120 + 20x) + 5X * (6 + x) + 4x * (6 + x) + xX(6 + x))(7 + x) = 1680
(120 + 20x + (6 * 5X + x * 5X) + 4x * (6 + x) + xX(6 + x))(7 + x) = 1680
(120 + 20x + (30X + 5xX) + 4x * (6 + x) + xX(6 + x))(7 + x) = 1680
(120 + 20x + 30X + 5xX + (6 * 4x + x * 4x) + xX(6 + x))(7 + x) = 1680
(120 + 20x + 30X + 5xX + (24x + 4x2) + xX(6 + x))(7 + x) = 1680
(120 + 20x + 30X + 5xX + 24x + 4x2 + (6 * xX + x * xX))(7 + x) = 1680
(120 + 20x + 30X + 5xX + 24x + 4x2 + (6xX + x2X))(7 + x) = 1680

Reorder the terms:
(120 + 30X + 20x + 24x + 5xX + 6xX + 4x2 + x2X)(7 + x) = 1680

Combine like terms: 20x + 24x = 44x
(120 + 30X + 44x + 5xX + 6xX + 4x2 + x2X)(7 + x) = 1680

Combine like terms: 5xX + 6xX = 11xX
(120 + 30X + 44x + 11xX + 4x2 + x2X)(7 + x) = 1680

Multiply (120 + 30X + 44x + 11xX + 4x2 + x2X) * (7 + x)
(120(7 + x) + 30X * (7 + x) + 44x * (7 + x) + 11xX * (7 + x) + 4x2 * (7 + x) + x2X(7 + x)) = 1680
((7 * 120 + x * 120) + 30X * (7 + x) + 44x * (7 + x) + 11xX * (7 + x) + 4x2 * (7 + x) + x2X(7 + x)) = 1680
((840 + 120x) + 30X * (7 + x) + 44x * (7 + x) + 11xX * (7 + x) + 4x2 * (7 + x) + x2X(7 + x)) = 1680
(840 + 120x + (7 * 30X + x * 30X) + 44x * (7 + x) + 11xX * (7 + x) + 4x2 * (7 + x) + x2X(7 + x)) = 1680
(840 + 120x + (210X + 30xX) + 44x * (7 + x) + 11xX * (7 + x) + 4x2 * (7 + x) + x2X(7 + x)) = 1680
(840 + 120x + 210X + 30xX + (7 * 44x + x * 44x) + 11xX * (7 + x) + 4x2 * (7 + x) + x2X(7 + x)) = 1680
(840 + 120x + 210X + 30xX + (308x + 44x2) + 11xX * (7 + x) + 4x2 * (7 + x) + x2X(7 + x)) = 1680
(840 + 120x + 210X + 30xX + 308x + 44x2 + (7 * 11xX + x * 11xX) + 4x2 * (7 + x) + x2X(7 + x)) = 1680
(840 + 120x + 210X + 30xX + 308x + 44x2 + (77xX + 11x2X) + 4x2 * (7 + x) + x2X(7 + x)) = 1680
(840 + 120x + 210X + 30xX + 308x + 44x2 + 77xX + 11x2X + (7 * 4x2 + x * 4x2) + x2X(7 + x)) = 1680
(840 + 120x + 210X + 30xX + 308x + 44x2 + 77xX + 11x2X + (28x2 + 4x3) + x2X(7 + x)) = 1680
(840 + 120x + 210X + 30xX + 308x + 44x2 + 77xX + 11x2X + 28x2 + 4x3 + (7 * x2X + x * x2X)) = 1680
(840 + 120x + 210X + 30xX + 308x + 44x2 + 77xX + 11x2X + 28x2 + 4x3 + (7x2X + x3X)) = 1680

Reorder the terms:
(840 + 210X + 120x + 308x + 30xX + 77xX + 44x2 + 28x2 + 11x2X + 7x2X + 4x3 + x3X) = 1680

Combine like terms: 120x + 308x = 428x
(840 + 210X + 428x + 30xX + 77xX + 44x2 + 28x2 + 11x2X + 7x2X + 4x3 + x3X) = 1680

Combine like terms: 30xX + 77xX = 107xX
(840 + 210X + 428x + 107xX + 44x2 + 28x2 + 11x2X + 7x2X + 4x3 + x3X) = 1680

Combine like terms: 44x2 + 28x2 = 72x2
(840 + 210X + 428x + 107xX + 72x2 + 11x2X + 7x2X + 4x3 + x3X) = 1680

Combine like terms: 11x2X + 7x2X = 18x2X
(840 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X) = 1680

Solving
840 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = 1680

Solving for variable 'X'.

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

Add '-840' to each side of the equation.
840 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + -840 + x3X = 1680 + -840

Reorder the terms:
840 + -840 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = 1680 + -840

Combine like terms: 840 + -840 = 0
0 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = 1680 + -840
210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = 1680 + -840

Combine like terms: 1680 + -840 = 840
210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = 840

Add '-428x' to each side of the equation.
210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + -428x + x3X = 840 + -428x

Reorder the terms:
210X + 428x + -428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = 840 + -428x

Combine like terms: 428x + -428x = 0
210X + 0 + 107xX + 72x2 + 18x2X + 4x3 + x3X = 840 + -428x
210X + 107xX + 72x2 + 18x2X + 4x3 + x3X = 840 + -428x

Add '-72x2' to each side of the equation.
210X + 107xX + 72x2 + 18x2X + 4x3 + -72x2 + x3X = 840 + -428x + -72x2

Reorder the terms:
210X + 107xX + 72x2 + -72x2 + 18x2X + 4x3 + x3X = 840 + -428x + -72x2

Combine like terms: 72x2 + -72x2 = 0
210X + 107xX + 0 + 18x2X + 4x3 + x3X = 840 + -428x + -72x2
210X + 107xX + 18x2X + 4x3 + x3X = 840 + -428x + -72x2

Add '-4x3' to each side of the equation.
210X + 107xX + 18x2X + 4x3 + -4x3 + x3X = 840 + -428x + -72x2 + -4x3

Combine like terms: 4x3 + -4x3 = 0
210X + 107xX + 18x2X + 0 + x3X = 840 + -428x + -72x2 + -4x3
210X + 107xX + 18x2X + x3X = 840 + -428x + -72x2 + -4x3

Reorder the terms:
-840 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = 840 + -428x + -72x2 + -4x3 + -840 + 428x + 72x2 + 4x3

Reorder the terms:
-840 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = 840 + -840 + -428x + 428x + -72x2 + 72x2 + -4x3 + 4x3

Combine like terms: 840 + -840 = 0
-840 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = 0 + -428x + 428x + -72x2 + 72x2 + -4x3 + 4x3
-840 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = -428x + 428x + -72x2 + 72x2 + -4x3 + 4x3

Combine like terms: -428x + 428x = 0
-840 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = 0 + -72x2 + 72x2 + -4x3 + 4x3
-840 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = -72x2 + 72x2 + -4x3 + 4x3

Combine like terms: -72x2 + 72x2 = 0
-840 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = 0 + -4x3 + 4x3
-840 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = -4x3 + 4x3

Combine like terms: -4x3 + 4x3 = 0
-840 + 210X + 428x + 107xX + 72x2 + 18x2X + 4x3 + x3X = 0

The solution to this equation could not be determined.

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