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Simplifying 2y(3y + 5)(2y + -7) = 0 Reorder the terms: 2y(5 + 3y)(2y + -7) = 0 Reorder the terms: 2y(5 + 3y)(-7 + 2y) = 0 Multiply (5 + 3y) * (-7 + 2y) 2y(5(-7 + 2y) + 3y * (-7 + 2y)) = 0 2y((-7 * 5 + 2y * 5) + 3y * (-7 + 2y)) = 0 2y((-35 + 10y) + 3y * (-7 + 2y)) = 0 2y(-35 + 10y + (-7 * 3y + 2y * 3y)) = 0 2y(-35 + 10y + (-21y + 6y2)) = 0 Combine like terms: 10y + -21y = -11y 2y(-35 + -11y + 6y2) = 0 (-35 * 2y + -11y * 2y + 6y2 * 2y) = 0 (-70y + -22y2 + 12y3) = 0 Solving -70y + -22y2 + 12y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(-35 + -11y + 6y2) = 0 Factor a trinomial. 2y((-5 + -3y)(7 + -2y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 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 = -1.666666667Subproblem 3
Set the factor '(7 + -2y)' equal to zero and attempt to solve: Simplifying 7 + -2y = 0 Solving 7 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2y = 0 + -7 -2y = 0 + -7 Combine like terms: 0 + -7 = -7 -2y = -7 Divide each side by '-2'. y = 3.5 Simplifying y = 3.5Solution
y = {0, -1.666666667, 3.5}
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