x^3+5x^2-12x+6=(x-1)(ax^2+bx+c)

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Solution for x^3+5x^2-12x+6=(x-1)(ax^2+bx+c) equation: 


Simplifying
x3 + 5x2 + -12x + 6 = (x + -1)(ax2 + bx + c)

Reorder the terms:
6 + -12x + 5x2 + x3 = (x + -1)(ax2 + bx + c)

Reorder the terms:
6 + -12x + 5x2 + x3 = (-1 + x)(ax2 + bx + c)

Multiply (-1 + x) * (ax2 + bx + c)
6 + -12x + 5x2 + x3 = (-1(ax2 + bx + c) + x(ax2 + bx + c))
6 + -12x + 5x2 + x3 = ((ax2 * -1 + bx * -1 + c * -1) + x(ax2 + bx + c))
6 + -12x + 5x2 + x3 = ((-1ax2 + -1bx + -1c) + x(ax2 + bx + c))
6 + -12x + 5x2 + x3 = (-1ax2 + -1bx + -1c + (ax2 * x + bx * x + c * x))
6 + -12x + 5x2 + x3 = (-1ax2 + -1bx + -1c + (ax3 + bx2 + cx))

Reorder the terms:
6 + -12x + 5x2 + x3 = (-1ax2 + ax3 + -1bx + bx2 + -1c + cx)
6 + -12x + 5x2 + x3 = (-1ax2 + ax3 + -1bx + bx2 + -1c + cx)

Solving
6 + -12x + 5x2 + x3 = -1ax2 + ax3 + -1bx + bx2 + -1c + cx

Solving for variable 'x'.

Reorder the terms:
6 + ax2 + -1ax3 + bx + -1bx2 + c + -1cx + -12x + 5x2 + x3 = -1ax2 + ax3 + -1bx + bx2 + -1c + cx + ax2 + -1ax3 + bx + -1bx2 + c + -1cx

Reorder the terms:
6 + ax2 + -1ax3 + bx + -1bx2 + c + -1cx + -12x + 5x2 + x3 = -1ax2 + ax2 + ax3 + -1ax3 + -1bx + bx + bx2 + -1bx2 + -1c + c + cx + -1cx

Combine like terms: -1ax2 + ax2 = 0
6 + ax2 + -1ax3 + bx + -1bx2 + c + -1cx + -12x + 5x2 + x3 = 0 + ax3 + -1ax3 + -1bx + bx + bx2 + -1bx2 + -1c + c + cx + -1cx
6 + ax2 + -1ax3 + bx + -1bx2 + c + -1cx + -12x + 5x2 + x3 = ax3 + -1ax3 + -1bx + bx + bx2 + -1bx2 + -1c + c + cx + -1cx

Combine like terms: ax3 + -1ax3 = 0
6 + ax2 + -1ax3 + bx + -1bx2 + c + -1cx + -12x + 5x2 + x3 = 0 + -1bx + bx + bx2 + -1bx2 + -1c + c + cx + -1cx
6 + ax2 + -1ax3 + bx + -1bx2 + c + -1cx + -12x + 5x2 + x3 = -1bx + bx + bx2 + -1bx2 + -1c + c + cx + -1cx

Combine like terms: -1bx + bx = 0
6 + ax2 + -1ax3 + bx + -1bx2 + c + -1cx + -12x + 5x2 + x3 = 0 + bx2 + -1bx2 + -1c + c + cx + -1cx
6 + ax2 + -1ax3 + bx + -1bx2 + c + -1cx + -12x + 5x2 + x3 = bx2 + -1bx2 + -1c + c + cx + -1cx

Combine like terms: bx2 + -1bx2 = 0
6 + ax2 + -1ax3 + bx + -1bx2 + c + -1cx + -12x + 5x2 + x3 = 0 + -1c + c + cx + -1cx
6 + ax2 + -1ax3 + bx + -1bx2 + c + -1cx + -12x + 5x2 + x3 = -1c + c + cx + -1cx

Combine like terms: -1c + c = 0
6 + ax2 + -1ax3 + bx + -1bx2 + c + -1cx + -12x + 5x2 + x3 = 0 + cx + -1cx
6 + ax2 + -1ax3 + bx + -1bx2 + c + -1cx + -12x + 5x2 + x3 = cx + -1cx

Combine like terms: cx + -1cx = 0
6 + ax2 + -1ax3 + bx + -1bx2 + c + -1cx + -12x + 5x2 + x3 = 0

The solution to this equation could not be determined.

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