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Simplifying -8y = 4y2 + 3 Reorder the terms: -8y = 3 + 4y2 Solving -8y = 3 + 4y2 Solving for variable 'y'. Reorder the terms: -3 + -8y + -4y2 = 3 + 4y2 + -3 + -4y2 Reorder the terms: -3 + -8y + -4y2 = 3 + -3 + 4y2 + -4y2 Combine like terms: 3 + -3 = 0 -3 + -8y + -4y2 = 0 + 4y2 + -4y2 -3 + -8y + -4y2 = 4y2 + -4y2 Combine like terms: 4y2 + -4y2 = 0 -3 + -8y + -4y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 8y + 4y2) = 0 Factor a trinomial. -1((3 + 2y)(1 + 2y)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 2y)' equal to zero and attempt to solve: Simplifying 3 + 2y = 0 Solving 3 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2y = 0 + -3 2y = 0 + -3 Combine like terms: 0 + -3 = -3 2y = -3 Divide each side by '2'. y = -1.5 Simplifying y = -1.5Subproblem 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 = {-1.5, -0.5}
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