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

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


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

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

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

Multiply (-2 + 5x) * (-1 + 2x)
(-2(-1 + 2x) + 5x * (-1 + 2x)) = 0
((-1 * -2 + 2x * -2) + 5x * (-1 + 2x)) = 0
((2 + -4x) + 5x * (-1 + 2x)) = 0
(2 + -4x + (-1 * 5x + 2x * 5x)) = 0
(2 + -4x + (-5x + 10x2)) = 0

Combine like terms: -4x + -5x = -9x
(2 + -9x + 10x2) = 0

Solving
2 + -9x + 10x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4

Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0.4, 0.5}

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