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

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


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

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

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

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

Combine like terms: -10x + -2x = -12x
2(5 + -12x + 4x2) = 0
(5 * 2 + -12x * 2 + 4x2 * 2) = 0
(10 + -24x + 8x2) = 0

Solving
10 + -24x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -12x + 4x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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 = {0.5, 2.5}

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