(x-2)(5-2x)=0

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Solution for (x-2)(5-2x)=0 equation: 


Simplifying
(x + -2)(5 + -2x) = 0

Reorder the terms:
(-2 + x)(5 + -2x) = 0

Multiply (-2 + x) * (5 + -2x)
(-2(5 + -2x) + x(5 + -2x)) = 0
((5 * -2 + -2x * -2) + x(5 + -2x)) = 0
((-10 + 4x) + x(5 + -2x)) = 0
(-10 + 4x + (5 * x + -2x * x)) = 0
(-10 + 4x + (5x + -2x2)) = 0

Combine like terms: 4x + 5x = 9x
(-10 + 9x + -2x2) = 0

Solving
-10 + 9x + -2x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {2.5, 2}

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