5(2-x)=2x(x-2)

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Solution for 5(2-x)=2x(x-2) equation: 


Simplifying
5(2 + -1x) = 2x(x + -2)
(2 * 5 + -1x * 5) = 2x(x + -2)
(10 + -5x) = 2x(x + -2)

Reorder the terms:
10 + -5x = 2x(-2 + x)
10 + -5x = (-2 * 2x + x * 2x)
10 + -5x = (-4x + 2x2)

Solving
10 + -5x = -4x + 2x2

Solving for variable 'x'.

Combine like terms: -5x + 4x = -1x
10 + -1x + -2x2 = -4x + 2x2 + 4x + -2x2

Reorder the terms:
10 + -1x + -2x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
10 + -1x + -2x2 = 0 + 2x2 + -2x2
10 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
10 + -1x + -2x2 = 0

Factor a trinomial.
(2 + -1x)(5 + 2x) = 0


Subproblem 1
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

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 = {2, -2.5}

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