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

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


Simplifying
(2 + -1x)(2x + -5) = 0

Reorder the terms:
(2 + -1x)(-5 + 2x) = 0

Multiply (2 + -1x) * (-5 + 2x)
(2(-5 + 2x) + -1x * (-5 + 2x)) = 0
((-5 * 2 + 2x * 2) + -1x * (-5 + 2x)) = 0
((-10 + 4x) + -1x * (-5 + 2x)) = 0
(-10 + 4x + (-5 * -1x + 2x * -1x)) = 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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