0=5x(2x-1)

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


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

Reorder the terms:
0 = 5x(-1 + 2x)
0 = (-1 * 5x + 2x * 5x)
0 = (-5x + 10x2)

Solving
0 = -5x + 10x2

Solving for variable 'x'.
Remove the zero:
5x + -10x2 = -5x + 10x2 + 5x + -10x2

Reorder the terms:
5x + -10x2 = -5x + 5x + 10x2 + -10x2

Combine like terms: -5x + 5x = 0
5x + -10x2 = 0 + 10x2 + -10x2
5x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
5x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(1 + -2x) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

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, 0.5}

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