x^3+1=(x+a)(x^2+bx+c)

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Solution for x^3+1=(x+a)(x^2+bx+c) equation: 


Simplifying
x3 + 1 = (x + a)(x2 + bx + c)

Reorder the terms:
1 + x3 = (x + a)(x2 + bx + c)

Reorder the terms:
1 + x3 = (a + x)(x2 + bx + c)

Reorder the terms:
1 + x3 = (a + x)(bx + c + x2)

Multiply (a + x) * (bx + c + x2)
1 + x3 = (a(bx + c + x2) + x(bx + c + x2))
1 + x3 = ((bx * a + c * a + x2 * a) + x(bx + c + x2))
1 + x3 = ((abx + ac + ax2) + x(bx + c + x2))
1 + x3 = (abx + ac + ax2 + (bx * x + c * x + x2 * x))
1 + x3 = (abx + ac + ax2 + (bx2 + cx + x3))
1 + x3 = (abx + ac + ax2 + bx2 + cx + x3)

Add '-1x3' to each side of the equation.
1 + x3 + -1x3 = abx + ac + ax2 + bx2 + cx + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
1 + 0 = abx + ac + ax2 + bx2 + cx + x3 + -1x3
1 = abx + ac + ax2 + bx2 + cx + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
1 = abx + ac + ax2 + bx2 + cx + 0
1 = abx + ac + ax2 + bx2 + cx

Solving
1 = abx + ac + ax2 + bx2 + cx

Solving for variable 'a'.

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

Add '-1abx' to each side of the equation.
1 + -1abx = abx + ac + ax2 + bx2 + -1abx + cx

Reorder the terms:
1 + -1abx = abx + -1abx + ac + ax2 + bx2 + cx

Combine like terms: abx + -1abx = 0
1 + -1abx = 0 + ac + ax2 + bx2 + cx
1 + -1abx = ac + ax2 + bx2 + cx

Add '-1ac' to each side of the equation.
1 + -1abx + -1ac = ac + ax2 + bx2 + -1ac + cx

Reorder the terms:
1 + -1abx + -1ac = ac + -1ac + ax2 + bx2 + cx

Combine like terms: ac + -1ac = 0
1 + -1abx + -1ac = 0 + ax2 + bx2 + cx
1 + -1abx + -1ac = ax2 + bx2 + cx

Add '-1ax2' to each side of the equation.
1 + -1abx + -1ac + -1ax2 = ax2 + bx2 + -1ax2 + cx

Reorder the terms:
1 + -1abx + -1ac + -1ax2 = ax2 + -1ax2 + bx2 + cx

Combine like terms: ax2 + -1ax2 = 0
1 + -1abx + -1ac + -1ax2 = 0 + bx2 + cx
1 + -1abx + -1ac + -1ax2 = bx2 + cx

Add '-1' to each side of the equation.
1 + -1abx + -1ac + -1 + -1ax2 = bx2 + -1 + cx

Reorder the terms:
1 + -1 + -1abx + -1ac + -1ax2 = bx2 + -1 + cx

Combine like terms: 1 + -1 = 0
0 + -1abx + -1ac + -1ax2 = bx2 + -1 + cx
-1abx + -1ac + -1ax2 = bx2 + -1 + cx

Reorder the terms:
-1abx + -1ac + -1ax2 = -1 + bx2 + cx

Reorder the terms:
1 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = -1 + bx2 + cx + 1 + -1bx2 + -1cx

Reorder the terms:
1 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = -1 + 1 + bx2 + -1bx2 + cx + -1cx

Combine like terms: -1 + 1 = 0
1 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = 0 + bx2 + -1bx2 + cx + -1cx
1 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = bx2 + -1bx2 + cx + -1cx

Combine like terms: bx2 + -1bx2 = 0
1 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = 0 + cx + -1cx
1 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = cx + -1cx

Combine like terms: cx + -1cx = 0
1 + -1abx + -1ac + -1ax2 + -1bx2 + -1cx = 0

The solution to this equation could not be determined.

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