(2y-1)(2y-1)=0

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Solution for (2y-1)(2y-1)=0 equation:


Simplifying
(2y + -1)(2y + -1) = 0

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

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

Multiply (-1 + 2y) * (-1 + 2y)
(-1(-1 + 2y) + 2y * (-1 + 2y)) = 0
((-1 * -1 + 2y * -1) + 2y * (-1 + 2y)) = 0
((1 + -2y) + 2y * (-1 + 2y)) = 0
(1 + -2y + (-1 * 2y + 2y * 2y)) = 0
(1 + -2y + (-2y + 4y2)) = 0

Combine like terms: -2y + -2y = -4y
(1 + -4y + 4y2) = 0

Solving
1 + -4y + 4y2 = 0

Solving for variable 'y'.

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

Subproblem 1

Set the factor '(1 + -2y)' equal to zero and attempt to solve: Simplifying 1 + -2y = 0 Solving 1 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2y = 0 + -1 -2y = 0 + -1 Combine like terms: 0 + -1 = -1 -2y = -1 Divide each side by '-2'. y = 0.5 Simplifying y = 0.5

Subproblem 2

Set the factor '(1 + -2y)' equal to zero and attempt to solve: Simplifying 1 + -2y = 0 Solving 1 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2y = 0 + -1 -2y = 0 + -1 Combine like terms: 0 + -1 = -1 -2y = -1 Divide each side by '-2'. y = 0.5 Simplifying y = 0.5

Solution

y = {0.5, 0.5}

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