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Simplifying (4y + 1)(2y + -1) = 0 Reorder the terms: (1 + 4y)(2y + -1) = 0 Reorder the terms: (1 + 4y)(-1 + 2y) = 0 Multiply (1 + 4y) * (-1 + 2y) (1(-1 + 2y) + 4y * (-1 + 2y)) = 0 ((-1 * 1 + 2y * 1) + 4y * (-1 + 2y)) = 0 ((-1 + 2y) + 4y * (-1 + 2y)) = 0 (-1 + 2y + (-1 * 4y + 2y * 4y)) = 0 (-1 + 2y + (-4y + 8y2)) = 0 Combine like terms: 2y + -4y = -2y (-1 + -2y + 8y2) = 0 Solving -1 + -2y + 8y2 = 0 Solving for variable 'y'. Factor a trinomial. (-1 + -4y)(1 + -2y) = 0Subproblem 1
Set the factor '(-1 + -4y)' equal to zero and attempt to solve: Simplifying -1 + -4y = 0 Solving -1 + -4y = 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 + -4y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4y = 0 + 1 -4y = 0 + 1 Combine like terms: 0 + 1 = 1 -4y = 1 Divide each side by '-4'. y = -0.25 Simplifying y = -0.25Subproblem 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 = 0.5Solution
y = {-0.25, 0.5}
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