(2x-5)(4x-10)=0

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Solution for (2x-5)(4x-10)=0 equation: 


Simplifying
(2x + -5)(4x + -10) = 0

Reorder the terms:
(-5 + 2x)(4x + -10) = 0

Reorder the terms:
(-5 + 2x)(-10 + 4x) = 0

Multiply (-5 + 2x) * (-10 + 4x)
(-5(-10 + 4x) + 2x * (-10 + 4x)) = 0
((-10 * -5 + 4x * -5) + 2x * (-10 + 4x)) = 0
((50 + -20x) + 2x * (-10 + 4x)) = 0
(50 + -20x + (-10 * 2x + 4x * 2x)) = 0
(50 + -20x + (-20x + 8x2)) = 0

Combine like terms: -20x + -20x = -40x
(50 + -40x + 8x2) = 0

Solving
50 + -40x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -20x + 4x2) = 0

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

Ignore the factor 2.

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 '(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 = {2.5, 2.5}

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