4x(x-2)=2x

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Solution for 4x(x-2)=2x equation: 


Simplifying
4x(x + -2) = 2x

Reorder the terms:
4x(-2 + x) = 2x
(-2 * 4x + x * 4x) = 2x
(-8x + 4x2) = 2x

Solving
-8x + 4x2 = 2x

Solving for variable 'x'.

Reorder the terms:
-8x + -2x + 4x2 = 2x + -2x

Combine like terms: -8x + -2x = -10x
-10x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-5 + 2x) = 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 '(-5 + 2x)' equal to zero and attempt to solve:

Simplifying
-5 + 2x = 0

Solving
-5 + 2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2x = 0 + 5
2x = 0 + 5

Combine like terms: 0 + 5 = 5
2x = 5

Divide each side by '2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, 2.5}

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