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

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


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

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

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

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

Combine like terms: -4x + -10x = -14x
(20 + -14x + 2x2) = 0

Solving
20 + -14x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -7x + x2) = 0

Factor a trinomial.
2((2 + -1x)(5 + -1x)) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {2, 5}

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