x^4-3x+2=(x-1)(x^3+bx^2+ax-2)

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Solution for x^4-3x+2=(x-1)(x^3+bx^2+ax-2) equation: 


Simplifying
x4 + -3x + 2 = (x + -1)(x3 + bx2 + ax + -2)

Reorder the terms:
2 + -3x + x4 = (x + -1)(x3 + bx2 + ax + -2)

Reorder the terms:
2 + -3x + x4 = (-1 + x)(x3 + bx2 + ax + -2)

Reorder the terms:
2 + -3x + x4 = (-1 + x)(-2 + ax + bx2 + x3)

Multiply (-1 + x) * (-2 + ax + bx2 + x3)
2 + -3x + x4 = (-1(-2 + ax + bx2 + x3) + x(-2 + ax + bx2 + x3))
2 + -3x + x4 = ((-2 * -1 + ax * -1 + bx2 * -1 + x3 * -1) + x(-2 + ax + bx2 + x3))
2 + -3x + x4 = ((2 + -1ax + -1bx2 + -1x3) + x(-2 + ax + bx2 + x3))
2 + -3x + x4 = (2 + -1ax + -1bx2 + -1x3 + (-2 * x + ax * x + bx2 * x + x3 * x))

Reorder the terms:
2 + -3x + x4 = (2 + -1ax + -1bx2 + -1x3 + (ax2 + bx3 + -2x + x4))
2 + -3x + x4 = (2 + -1ax + -1bx2 + -1x3 + (ax2 + bx3 + -2x + x4))

Reorder the terms:
2 + -3x + x4 = (2 + -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + x4)
2 + -3x + x4 = (2 + -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + x4)

Add '-2' to each side of the equation.
2 + -3x + -2 + x4 = 2 + -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + -2 + x4

Reorder the terms:
2 + -2 + -3x + x4 = 2 + -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + -2 + x4

Combine like terms: 2 + -2 = 0
0 + -3x + x4 = 2 + -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + -2 + x4
-3x + x4 = 2 + -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + -2 + x4

Reorder the terms:
-3x + x4 = 2 + -2 + -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + x4

Combine like terms: 2 + -2 = 0
-3x + x4 = 0 + -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + x4
-3x + x4 = -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + x4

Add '-1x4' to each side of the equation.
-3x + x4 + -1x4 = -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-3x + 0 = -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + x4 + -1x4
-3x = -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-3x = -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + 0
-3x = -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3

Solving
-3x = -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3

Solving for variable 'x'.

Reorder the terms:
ax + -1ax2 + bx2 + -1bx3 + -3x + 2x + x3 = -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + ax + -1ax2 + bx2 + -1bx3 + 2x + x3

Combine like terms: -3x + 2x = -1x
ax + -1ax2 + bx2 + -1bx3 + -1x + x3 = -1ax + ax2 + -1bx2 + bx3 + -2x + -1x3 + ax + -1ax2 + bx2 + -1bx3 + 2x + x3

Reorder the terms:
ax + -1ax2 + bx2 + -1bx3 + -1x + x3 = -1ax + ax + ax2 + -1ax2 + -1bx2 + bx2 + bx3 + -1bx3 + -2x + 2x + -1x3 + x3

Combine like terms: -1ax + ax = 0
ax + -1ax2 + bx2 + -1bx3 + -1x + x3 = 0 + ax2 + -1ax2 + -1bx2 + bx2 + bx3 + -1bx3 + -2x + 2x + -1x3 + x3
ax + -1ax2 + bx2 + -1bx3 + -1x + x3 = ax2 + -1ax2 + -1bx2 + bx2 + bx3 + -1bx3 + -2x + 2x + -1x3 + x3

Combine like terms: ax2 + -1ax2 = 0
ax + -1ax2 + bx2 + -1bx3 + -1x + x3 = 0 + -1bx2 + bx2 + bx3 + -1bx3 + -2x + 2x + -1x3 + x3
ax + -1ax2 + bx2 + -1bx3 + -1x + x3 = -1bx2 + bx2 + bx3 + -1bx3 + -2x + 2x + -1x3 + x3

Combine like terms: -1bx2 + bx2 = 0
ax + -1ax2 + bx2 + -1bx3 + -1x + x3 = 0 + bx3 + -1bx3 + -2x + 2x + -1x3 + x3
ax + -1ax2 + bx2 + -1bx3 + -1x + x3 = bx3 + -1bx3 + -2x + 2x + -1x3 + x3

Combine like terms: bx3 + -1bx3 = 0
ax + -1ax2 + bx2 + -1bx3 + -1x + x3 = 0 + -2x + 2x + -1x3 + x3
ax + -1ax2 + bx2 + -1bx3 + -1x + x3 = -2x + 2x + -1x3 + x3

Combine like terms: -2x + 2x = 0
ax + -1ax2 + bx2 + -1bx3 + -1x + x3 = 0 + -1x3 + x3
ax + -1ax2 + bx2 + -1bx3 + -1x + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
ax + -1ax2 + bx2 + -1bx3 + -1x + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(a + -1ax + bx + -1bx2 + -1 + x2) = 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 '(a + -1ax + bx + -1bx2 + -1 + x2)' equal to zero and attempt to solve:

Simplifying
a + -1ax + bx + -1bx2 + -1 + x2 = 0

Reorder the terms:
-1 + a + -1ax + bx + -1bx2 + x2 = 0

Solving
-1 + a + -1ax + bx + -1bx2 + x2 = 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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