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

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


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

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

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

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

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

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

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

Multiply (3 + x) * (-2 + x)
-4 + -2x + 2x2 = (3(-2 + x) + x(-2 + x))
-4 + -2x + 2x2 = ((-2 * 3 + x * 3) + x(-2 + x))
-4 + -2x + 2x2 = ((-6 + 3x) + x(-2 + x))
-4 + -2x + 2x2 = (-6 + 3x + (-2 * x + x * x))
-4 + -2x + 2x2 = (-6 + 3x + (-2x + x2))

Combine like terms: 3x + -2x = 1x
-4 + -2x + 2x2 = (-6 + 1x + x2)

Solving
-4 + -2x + 2x2 = -6 + 1x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + 6 + -2x + -1x + 2x2 + -1x2 = -6 + 1x + x2 + 6 + -1x + -1x2

Combine like terms: -4 + 6 = 2
2 + -2x + -1x + 2x2 + -1x2 = -6 + 1x + x2 + 6 + -1x + -1x2

Combine like terms: -2x + -1x = -3x
2 + -3x + 2x2 + -1x2 = -6 + 1x + x2 + 6 + -1x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
2 + -3x + 1x2 = -6 + 1x + x2 + 6 + -1x + -1x2

Reorder the terms:
2 + -3x + 1x2 = -6 + 6 + 1x + -1x + x2 + -1x2

Combine like terms: -6 + 6 = 0
2 + -3x + 1x2 = 0 + 1x + -1x + x2 + -1x2
2 + -3x + 1x2 = 1x + -1x + x2 + -1x2

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

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

Factor a trinomial.
(1 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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
Solution
x = {1, 2}

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