(2x-5)(4x-1)=0

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Solution for (2x-5)(4x-1)=0 equation: 


Simplifying
(2x + -5)(4x + -1) = 0

Reorder the terms:
(-5 + 2x)(4x + -1) = 0

Reorder the terms:
(-5 + 2x)(-1 + 4x) = 0

Multiply (-5 + 2x) * (-1 + 4x)
(-5(-1 + 4x) + 2x * (-1 + 4x)) = 0
((-1 * -5 + 4x * -5) + 2x * (-1 + 4x)) = 0
((5 + -20x) + 2x * (-1 + 4x)) = 0
(5 + -20x + (-1 * 2x + 4x * 2x)) = 0
(5 + -20x + (-2x + 8x2)) = 0

Combine like terms: -20x + -2x = -22x
(5 + -22x + 8x2) = 0

Solving
5 + -22x + 8x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -4x)(5 + -2x) = 0


Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

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 = {0.25, 2.5}

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