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Simplifying 0 = 4y2 + -23y + 33 Reorder the terms: 0 = 33 + -23y + 4y2 Solving 0 = 33 + -23y + 4y2 Solving for variable 'y'. Combine like terms: 0 + -33 = -33 -33 + 23y + -4y2 = 33 + -23y + 4y2 + -33 + 23y + -4y2 Reorder the terms: -33 + 23y + -4y2 = 33 + -33 + -23y + 23y + 4y2 + -4y2 Combine like terms: 33 + -33 = 0 -33 + 23y + -4y2 = 0 + -23y + 23y + 4y2 + -4y2 -33 + 23y + -4y2 = -23y + 23y + 4y2 + -4y2 Combine like terms: -23y + 23y = 0 -33 + 23y + -4y2 = 0 + 4y2 + -4y2 -33 + 23y + -4y2 = 4y2 + -4y2 Combine like terms: 4y2 + -4y2 = 0 -33 + 23y + -4y2 = 0 Factor a trinomial. (-3 + y)(11 + -4y) = 0Subproblem 1
Set the factor '(-3 + y)' equal to zero and attempt to solve: Simplifying -3 + y = 0 Solving -3 + y = 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 + y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + y = 0 + 3 y = 0 + 3 Combine like terms: 0 + 3 = 3 y = 3 Simplifying y = 3Subproblem 2
Set the factor '(11 + -4y)' equal to zero and attempt to solve: Simplifying 11 + -4y = 0 Solving 11 + -4y = 0 Move all terms containing y to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -4y = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -4y = 0 + -11 -4y = 0 + -11 Combine like terms: 0 + -11 = -11 -4y = -11 Divide each side by '-4'. y = 2.75 Simplifying y = 2.75Solution
y = {3, 2.75}
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