x^3+10x+21=(x+3)(x+a)

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Solution for x^3+10x+21=(x+3)(x+a) equation: 


Simplifying
x3 + 10x + 21 = (x + 3)(x + a)

Reorder the terms:
21 + 10x + x3 = (x + 3)(x + a)

Reorder the terms:
21 + 10x + x3 = (3 + x)(x + a)

Reorder the terms:
21 + 10x + x3 = (3 + x)(a + x)

Multiply (3 + x) * (a + x)
21 + 10x + x3 = (3(a + x) + x(a + x))
21 + 10x + x3 = ((a * 3 + x * 3) + x(a + x))
21 + 10x + x3 = ((3a + 3x) + x(a + x))
21 + 10x + x3 = (3a + 3x + (a * x + x * x))
21 + 10x + x3 = (3a + 3x + (ax + x2))

Reorder the terms:
21 + 10x + x3 = (3a + ax + 3x + x2)
21 + 10x + x3 = (3a + ax + 3x + x2)

Solving
21 + 10x + x3 = 3a + ax + 3x + x2

Solving for variable 'x'.

Reorder the terms:
21 + -3a + -1ax + 10x + -3x + -1x2 + x3 = 3a + ax + 3x + x2 + -3a + -1ax + -3x + -1x2

Combine like terms: 10x + -3x = 7x
21 + -3a + -1ax + 7x + -1x2 + x3 = 3a + ax + 3x + x2 + -3a + -1ax + -3x + -1x2

Reorder the terms:
21 + -3a + -1ax + 7x + -1x2 + x3 = 3a + -3a + ax + -1ax + 3x + -3x + x2 + -1x2

Combine like terms: 3a + -3a = 0
21 + -3a + -1ax + 7x + -1x2 + x3 = 0 + ax + -1ax + 3x + -3x + x2 + -1x2
21 + -3a + -1ax + 7x + -1x2 + x3 = ax + -1ax + 3x + -3x + x2 + -1x2

Combine like terms: ax + -1ax = 0
21 + -3a + -1ax + 7x + -1x2 + x3 = 0 + 3x + -3x + x2 + -1x2
21 + -3a + -1ax + 7x + -1x2 + x3 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
21 + -3a + -1ax + 7x + -1x2 + x3 = 0 + x2 + -1x2
21 + -3a + -1ax + 7x + -1x2 + x3 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
21 + -3a + -1ax + 7x + -1x2 + x3 = 0

The solution to this equation could not be determined.

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