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Simplifying 2y2 = y + 6 Reorder the terms: 2y2 = 6 + y Solving 2y2 = 6 + y Solving for variable 'y'. Reorder the terms: -6 + -1y + 2y2 = 6 + y + -6 + -1y Reorder the terms: -6 + -1y + 2y2 = 6 + -6 + y + -1y Combine like terms: 6 + -6 = 0 -6 + -1y + 2y2 = 0 + y + -1y -6 + -1y + 2y2 = y + -1y Combine like terms: y + -1y = 0 -6 + -1y + 2y2 = 0 Factor a trinomial. (-3 + -2y)(2 + -1y) = 0Subproblem 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 '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2Solution
y = {-1.5, 2}
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