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Simplifying (6 + y)(3y + -5) = 0 Reorder the terms: (6 + y)(-5 + 3y) = 0 Multiply (6 + y) * (-5 + 3y) (6(-5 + 3y) + y(-5 + 3y)) = 0 ((-5 * 6 + 3y * 6) + y(-5 + 3y)) = 0 ((-30 + 18y) + y(-5 + 3y)) = 0 (-30 + 18y + (-5 * y + 3y * y)) = 0 (-30 + 18y + (-5y + 3y2)) = 0 Combine like terms: 18y + -5y = 13y (-30 + 13y + 3y2) = 0 Solving -30 + 13y + 3y2 = 0 Solving for variable 'y'. Factor a trinomial. (-6 + -1y)(5 + -3y) = 0Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve: Simplifying -6 + -1y = 0 Solving -6 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1y = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1y = 0 + 6 -1y = 0 + 6 Combine like terms: 0 + 6 = 6 -1y = 6 Divide each side by '-1'. y = -6 Simplifying y = -6Subproblem 2
Set the factor '(5 + -3y)' equal to zero and attempt to solve: Simplifying 5 + -3y = 0 Solving 5 + -3y = 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 + -3y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3y = 0 + -5 -3y = 0 + -5 Combine like terms: 0 + -5 = -5 -3y = -5 Divide each side by '-3'. y = 1.666666667 Simplifying y = 1.666666667Solution
y = {-6, 1.666666667}
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