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

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


Simplifying
(x + -1)(x + 1)(x + -2) + x(2x + -3) = x3 + -4(x + 2)

Reorder the terms:
(-1 + x)(x + 1)(x + -2) + x(2x + -3) = x3 + -4(x + 2)

Reorder the terms:
(-1 + x)(1 + x)(x + -2) + x(2x + -3) = x3 + -4(x + 2)

Reorder the terms:
(-1 + x)(1 + x)(-2 + x) + x(2x + -3) = x3 + -4(x + 2)

Multiply (-1 + x) * (1 + x)
(-1(1 + x) + x(1 + x))(-2 + x) + x(2x + -3) = x3 + -4(x + 2)
((1 * -1 + x * -1) + x(1 + x))(-2 + x) + x(2x + -3) = x3 + -4(x + 2)
((-1 + -1x) + x(1 + x))(-2 + x) + x(2x + -3) = x3 + -4(x + 2)
(-1 + -1x + (1 * x + x * x))(-2 + x) + x(2x + -3) = x3 + -4(x + 2)
(-1 + -1x + (1x + x2))(-2 + x) + x(2x + -3) = x3 + -4(x + 2)

Combine like terms: -1x + 1x = 0
(-1 + 0 + x2)(-2 + x) + x(2x + -3) = x3 + -4(x + 2)
(-1 + x2)(-2 + x) + x(2x + -3) = x3 + -4(x + 2)

Multiply (-1 + x2) * (-2 + x)
(-1(-2 + x) + x2(-2 + x)) + x(2x + -3) = x3 + -4(x + 2)
((-2 * -1 + x * -1) + x2(-2 + x)) + x(2x + -3) = x3 + -4(x + 2)
((2 + -1x) + x2(-2 + x)) + x(2x + -3) = x3 + -4(x + 2)
(2 + -1x + (-2 * x2 + x * x2)) + x(2x + -3) = x3 + -4(x + 2)
(2 + -1x + (-2x2 + x3)) + x(2x + -3) = x3 + -4(x + 2)
(2 + -1x + -2x2 + x3) + x(2x + -3) = x3 + -4(x + 2)

Reorder the terms:
2 + -1x + -2x2 + x3 + x(-3 + 2x) = x3 + -4(x + 2)
2 + -1x + -2x2 + x3 + (-3 * x + 2x * x) = x3 + -4(x + 2)
2 + -1x + -2x2 + x3 + (-3x + 2x2) = x3 + -4(x + 2)

Reorder the terms:
2 + -1x + -3x + -2x2 + 2x2 + x3 = x3 + -4(x + 2)

Combine like terms: -1x + -3x = -4x
2 + -4x + -2x2 + 2x2 + x3 = x3 + -4(x + 2)

Combine like terms: -2x2 + 2x2 = 0
2 + -4x + 0 + x3 = x3 + -4(x + 2)
2 + -4x + x3 = x3 + -4(x + 2)

Reorder the terms:
2 + -4x + x3 = x3 + -4(2 + x)
2 + -4x + x3 = x3 + (2 * -4 + x * -4)
2 + -4x + x3 = x3 + (-8 + -4x)

Reorder the terms:
2 + -4x + x3 = -8 + -4x + x3

Add '4x' to each side of the equation.
2 + -4x + 4x + x3 = -8 + -4x + 4x + x3

Combine like terms: -4x + 4x = 0
2 + 0 + x3 = -8 + -4x + 4x + x3
2 + x3 = -8 + -4x + 4x + x3

Combine like terms: -4x + 4x = 0
2 + x3 = -8 + 0 + x3
2 + x3 = -8 + x3

Add '-1x3' to each side of the equation.
2 + x3 + -1x3 = -8 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
2 + 0 = -8 + x3 + -1x3
2 = -8 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
2 = -8 + 0
2 = -8

Solving
2 = -8

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

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