(2x-1)(2+x)-(x+1)(3x-2)=0

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Solution for (2x-1)(2+x)-(x+1)(3x-2)=0 equation:


Simplifying
(2x + -1)(2 + x) + -1(x + 1)(3x + -2) = 0

Reorder the terms:
(-1 + 2x)(2 + x) + -1(x + 1)(3x + -2) = 0

Multiply (-1 + 2x) * (2 + x)
(-1(2 + x) + 2x * (2 + x)) + -1(x + 1)(3x + -2) = 0
((2 * -1 + x * -1) + 2x * (2 + x)) + -1(x + 1)(3x + -2) = 0
((-2 + -1x) + 2x * (2 + x)) + -1(x + 1)(3x + -2) = 0
(-2 + -1x + (2 * 2x + x * 2x)) + -1(x + 1)(3x + -2) = 0
(-2 + -1x + (4x + 2x2)) + -1(x + 1)(3x + -2) = 0

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

Reorder the terms:
-2 + 3x + 2x2 + -1(1 + x)(3x + -2) = 0

Reorder the terms:
-2 + 3x + 2x2 + -1(1 + x)(-2 + 3x) = 0

Multiply (1 + x) * (-2 + 3x)
-2 + 3x + 2x2 + -1(1(-2 + 3x) + x(-2 + 3x)) = 0
-2 + 3x + 2x2 + -1((-2 * 1 + 3x * 1) + x(-2 + 3x)) = 0
-2 + 3x + 2x2 + -1((-2 + 3x) + x(-2 + 3x)) = 0
-2 + 3x + 2x2 + -1(-2 + 3x + (-2 * x + 3x * x)) = 0
-2 + 3x + 2x2 + -1(-2 + 3x + (-2x + 3x2)) = 0

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

Reorder the terms:
-2 + 2 + 3x + -1x + 2x2 + -3x2 = 0

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

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

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

Solving
2x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(2 + -1x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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 = {0, 2}

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