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

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


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

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

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

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 3 + -4x + -3 + 2x2

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

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

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

Solving
-2x = -4x + 2x2

Solving for variable 'x'.

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

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

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

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

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

Ignore the factor 2.

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 '(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
Solution
x = {0, 1}

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