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

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


Simplifying
2x3 + -1x2 + 4x + -2 = (2x + 1)(ax2 + bx + c)

Reorder the terms:
-2 + 4x + -1x2 + 2x3 = (2x + 1)(ax2 + bx + c)

Reorder the terms:
-2 + 4x + -1x2 + 2x3 = (1 + 2x)(ax2 + bx + c)

Multiply (1 + 2x) * (ax2 + bx + c)
-2 + 4x + -1x2 + 2x3 = (1(ax2 + bx + c) + 2x * (ax2 + bx + c))
-2 + 4x + -1x2 + 2x3 = ((ax2 * 1 + bx * 1 + c * 1) + 2x * (ax2 + bx + c))
-2 + 4x + -1x2 + 2x3 = ((1ax2 + 1bx + 1c) + 2x * (ax2 + bx + c))
-2 + 4x + -1x2 + 2x3 = (1ax2 + 1bx + 1c + (ax2 * 2x + bx * 2x + c * 2x))
-2 + 4x + -1x2 + 2x3 = (1ax2 + 1bx + 1c + (2ax3 + 2bx2 + 2cx))

Reorder the terms:
-2 + 4x + -1x2 + 2x3 = (1ax2 + 2ax3 + 1bx + 2bx2 + 1c + 2cx)
-2 + 4x + -1x2 + 2x3 = (1ax2 + 2ax3 + 1bx + 2bx2 + 1c + 2cx)

Solving
-2 + 4x + -1x2 + 2x3 = 1ax2 + 2ax3 + 1bx + 2bx2 + 1c + 2cx

Solving for variable 'x'.

Reorder the terms:
-2 + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx + 4x + -1x2 + 2x3 = 1ax2 + 2ax3 + 1bx + 2bx2 + 1c + 2cx + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx

Reorder the terms:
-2 + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx + 4x + -1x2 + 2x3 = 1ax2 + -1ax2 + 2ax3 + -2ax3 + 1bx + -1bx + 2bx2 + -2bx2 + 1c + -1c + 2cx + -2cx

Combine like terms: 1ax2 + -1ax2 = 0
-2 + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx + 4x + -1x2 + 2x3 = 0 + 2ax3 + -2ax3 + 1bx + -1bx + 2bx2 + -2bx2 + 1c + -1c + 2cx + -2cx
-2 + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx + 4x + -1x2 + 2x3 = 2ax3 + -2ax3 + 1bx + -1bx + 2bx2 + -2bx2 + 1c + -1c + 2cx + -2cx

Combine like terms: 2ax3 + -2ax3 = 0
-2 + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx + 4x + -1x2 + 2x3 = 0 + 1bx + -1bx + 2bx2 + -2bx2 + 1c + -1c + 2cx + -2cx
-2 + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx + 4x + -1x2 + 2x3 = 1bx + -1bx + 2bx2 + -2bx2 + 1c + -1c + 2cx + -2cx

Combine like terms: 1bx + -1bx = 0
-2 + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx + 4x + -1x2 + 2x3 = 0 + 2bx2 + -2bx2 + 1c + -1c + 2cx + -2cx
-2 + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx + 4x + -1x2 + 2x3 = 2bx2 + -2bx2 + 1c + -1c + 2cx + -2cx

Combine like terms: 2bx2 + -2bx2 = 0
-2 + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx + 4x + -1x2 + 2x3 = 0 + 1c + -1c + 2cx + -2cx
-2 + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx + 4x + -1x2 + 2x3 = 1c + -1c + 2cx + -2cx

Combine like terms: 1c + -1c = 0
-2 + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx + 4x + -1x2 + 2x3 = 0 + 2cx + -2cx
-2 + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx + 4x + -1x2 + 2x3 = 2cx + -2cx

Combine like terms: 2cx + -2cx = 0
-2 + -1ax2 + -2ax3 + -1bx + -2bx2 + -1c + -2cx + 4x + -1x2 + 2x3 = 0

The solution to this equation could not be determined.

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