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

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


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

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

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

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

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

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

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

Combine like terms: -3x + -2x = -5x
-2 + -5x + 2x2 + -1x2 = (x + -1)(x + 3)

Combine like terms: 2x2 + -1x2 = 1x2
-2 + -5x + 1x2 = (x + -1)(x + 3)

Reorder the terms:
-2 + -5x + 1x2 = (-1 + x)(x + 3)

Reorder the terms:
-2 + -5x + 1x2 = (-1 + x)(3 + x)

Multiply (-1 + x) * (3 + x)
-2 + -5x + 1x2 = (-1(3 + x) + x(3 + x))
-2 + -5x + 1x2 = ((3 * -1 + x * -1) + x(3 + x))
-2 + -5x + 1x2 = ((-3 + -1x) + x(3 + x))
-2 + -5x + 1x2 = (-3 + -1x + (3 * x + x * x))
-2 + -5x + 1x2 = (-3 + -1x + (3x + x2))

Combine like terms: -1x + 3x = 2x
-2 + -5x + 1x2 = (-3 + 2x + x2)

Solving
-2 + -5x + 1x2 = -3 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-2 + 3 + -5x + -2x + 1x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Combine like terms: -2 + 3 = 1
1 + -5x + -2x + 1x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Combine like terms: -5x + -2x = -7x
1 + -7x + 1x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Combine like terms: 1x2 + -1x2 = 0
1 + -7x + 0 = -3 + 2x + x2 + 3 + -2x + -1x2
1 + -7x = -3 + 2x + x2 + 3 + -2x + -1x2

Reorder the terms:
1 + -7x = -3 + 3 + 2x + -2x + x2 + -1x2

Combine like terms: -3 + 3 = 0
1 + -7x = 0 + 2x + -2x + x2 + -1x2
1 + -7x = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
1 + -7x = 0 + x2 + -1x2
1 + -7x = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1 + -7x = 0

The solution to this equation could not be determined.

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