(2x-5)(2x-4)=0

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Solution for (2x-5)(2x-4)=0 equation: 


Simplifying
(2x + -5)(2x + -4) = 0

Reorder the terms:
(-5 + 2x)(2x + -4) = 0

Reorder the terms:
(-5 + 2x)(-4 + 2x) = 0

Multiply (-5 + 2x) * (-4 + 2x)
(-5(-4 + 2x) + 2x * (-4 + 2x)) = 0
((-4 * -5 + 2x * -5) + 2x * (-4 + 2x)) = 0
((20 + -10x) + 2x * (-4 + 2x)) = 0
(20 + -10x + (-4 * 2x + 2x * 2x)) = 0
(20 + -10x + (-8x + 4x2)) = 0

Combine like terms: -10x + -8x = -18x
(20 + -18x + 4x2) = 0

Solving
20 + -18x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -9x + 2x2) = 0

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

Ignore the factor 2.

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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