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

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


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

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

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

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

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

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

Add '-2x2' to each side of the equation.
-2 + -1x + 2x2 + -2x2 = -2x + 2x2 + -2x2

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

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

Solving
-2 + -1x = -2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

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

Combine like terms: -1x + 2x = 1x
-2 + 1x = -2x + 2x

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

Add '2' to each side of the equation.
-2 + 2 + 1x = 0 + 2

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

Combine like terms: 0 + 2 = 2
1x = 2

Divide each side by '1'.
x = 2

Simplifying
x = 2

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