(x+3)(x+a)(x+7)=x^3+15x^2+71x+105

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Solution for (x+3)(x+a)(x+7)=x^3+15x^2+71x+105 equation: 


Simplifying
(x + 3)(x + a)(x + 7) = x3 + 15x2 + 71x + 105

Reorder the terms:
(3 + x)(x + a)(x + 7) = x3 + 15x2 + 71x + 105

Reorder the terms:
(3 + x)(a + x)(x + 7) = x3 + 15x2 + 71x + 105

Reorder the terms:
(3 + x)(a + x)(7 + x) = x3 + 15x2 + 71x + 105

Multiply (3 + x) * (a + x)
(3(a + x) + x(a + x))(7 + x) = x3 + 15x2 + 71x + 105
((a * 3 + x * 3) + x(a + x))(7 + x) = x3 + 15x2 + 71x + 105
((3a + 3x) + x(a + x))(7 + x) = x3 + 15x2 + 71x + 105
(3a + 3x + (a * x + x * x))(7 + x) = x3 + 15x2 + 71x + 105
(3a + 3x + (ax + x2))(7 + x) = x3 + 15x2 + 71x + 105

Reorder the terms:
(3a + ax + 3x + x2)(7 + x) = x3 + 15x2 + 71x + 105
(3a + ax + 3x + x2)(7 + x) = x3 + 15x2 + 71x + 105

Multiply (3a + ax + 3x + x2) * (7 + x)
(3a * (7 + x) + ax(7 + x) + 3x * (7 + x) + x2(7 + x)) = x3 + 15x2 + 71x + 105
((7 * 3a + x * 3a) + ax(7 + x) + 3x * (7 + x) + x2(7 + x)) = x3 + 15x2 + 71x + 105
((21a + 3ax) + ax(7 + x) + 3x * (7 + x) + x2(7 + x)) = x3 + 15x2 + 71x + 105
(21a + 3ax + (7 * ax + x * ax) + 3x * (7 + x) + x2(7 + x)) = x3 + 15x2 + 71x + 105
(21a + 3ax + (7ax + ax2) + 3x * (7 + x) + x2(7 + x)) = x3 + 15x2 + 71x + 105
(21a + 3ax + 7ax + ax2 + (7 * 3x + x * 3x) + x2(7 + x)) = x3 + 15x2 + 71x + 105
(21a + 3ax + 7ax + ax2 + (21x + 3x2) + x2(7 + x)) = x3 + 15x2 + 71x + 105
(21a + 3ax + 7ax + ax2 + 21x + 3x2 + (7 * x2 + x * x2)) = x3 + 15x2 + 71x + 105
(21a + 3ax + 7ax + ax2 + 21x + 3x2 + (7x2 + x3)) = x3 + 15x2 + 71x + 105

Combine like terms: 3ax + 7ax = 10ax
(21a + 10ax + ax2 + 21x + 3x2 + 7x2 + x3) = x3 + 15x2 + 71x + 105

Combine like terms: 3x2 + 7x2 = 10x2
(21a + 10ax + ax2 + 21x + 10x2 + x3) = x3 + 15x2 + 71x + 105

Reorder the terms:
21a + 10ax + ax2 + 21x + 10x2 + x3 = 105 + 71x + 15x2 + x3

Add '-1x3' to each side of the equation.
21a + 10ax + ax2 + 21x + 10x2 + x3 + -1x3 = 105 + 71x + 15x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
21a + 10ax + ax2 + 21x + 10x2 + 0 = 105 + 71x + 15x2 + x3 + -1x3
21a + 10ax + ax2 + 21x + 10x2 = 105 + 71x + 15x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
21a + 10ax + ax2 + 21x + 10x2 = 105 + 71x + 15x2 + 0
21a + 10ax + ax2 + 21x + 10x2 = 105 + 71x + 15x2

Solving
21a + 10ax + ax2 + 21x + 10x2 = 105 + 71x + 15x2

Solving for variable 'a'.

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

Add '-21x' to each side of the equation.
21a + 10ax + ax2 + 21x + -21x + 10x2 = 105 + 71x + -21x + 15x2

Combine like terms: 21x + -21x = 0
21a + 10ax + ax2 + 0 + 10x2 = 105 + 71x + -21x + 15x2
21a + 10ax + ax2 + 10x2 = 105 + 71x + -21x + 15x2

Combine like terms: 71x + -21x = 50x
21a + 10ax + ax2 + 10x2 = 105 + 50x + 15x2

Add '-10x2' to each side of the equation.
21a + 10ax + ax2 + 10x2 + -10x2 = 105 + 50x + 15x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
21a + 10ax + ax2 + 0 = 105 + 50x + 15x2 + -10x2
21a + 10ax + ax2 = 105 + 50x + 15x2 + -10x2

Combine like terms: 15x2 + -10x2 = 5x2
21a + 10ax + ax2 = 105 + 50x + 5x2

Reorder the terms:
-105 + 21a + 10ax + ax2 + -50x + -5x2 = 105 + 50x + 5x2 + -105 + -50x + -5x2

Reorder the terms:
-105 + 21a + 10ax + ax2 + -50x + -5x2 = 105 + -105 + 50x + -50x + 5x2 + -5x2

Combine like terms: 105 + -105 = 0
-105 + 21a + 10ax + ax2 + -50x + -5x2 = 0 + 50x + -50x + 5x2 + -5x2
-105 + 21a + 10ax + ax2 + -50x + -5x2 = 50x + -50x + 5x2 + -5x2

Combine like terms: 50x + -50x = 0
-105 + 21a + 10ax + ax2 + -50x + -5x2 = 0 + 5x2 + -5x2
-105 + 21a + 10ax + ax2 + -50x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-105 + 21a + 10ax + ax2 + -50x + -5x2 = 0

The solution to this equation could not be determined.

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