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Simplifying (3y + -4y + 5)(y + -3y + 3) = 0 Reorder the terms: (5 + 3y + -4y)(y + -3y + 3) = 0 Combine like terms: 3y + -4y = -1y (5 + -1y)(y + -3y + 3) = 0 Reorder the terms: (5 + -1y)(3 + y + -3y) = 0 Combine like terms: y + -3y = -2y (5 + -1y)(3 + -2y) = 0 Multiply (5 + -1y) * (3 + -2y) (5(3 + -2y) + -1y * (3 + -2y)) = 0 ((3 * 5 + -2y * 5) + -1y * (3 + -2y)) = 0 ((15 + -10y) + -1y * (3 + -2y)) = 0 (15 + -10y + (3 * -1y + -2y * -1y)) = 0 (15 + -10y + (-3y + 2y2)) = 0 Combine like terms: -10y + -3y = -13y (15 + -13y + 2y2) = 0 Solving 15 + -13y + 2y2 = 0 Solving for variable 'y'. Factor a trinomial. (3 + -2y)(5 + -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 '(5 + -1y)' equal to zero and attempt to solve: Simplifying 5 + -1y = 0 Solving 5 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1y = 0 + -5 -1y = 0 + -5 Combine like terms: 0 + -5 = -5 -1y = -5 Divide each side by '-1'. y = 5 Simplifying y = 5Solution
y = {1.5, 5}
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