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Simplifying 5y(y + 7)(y + 3) = 0 Reorder the terms: 5y(7 + y)(y + 3) = 0 Reorder the terms: 5y(7 + y)(3 + y) = 0 Multiply (7 + y) * (3 + y) 5y(7(3 + y) + y(3 + y)) = 0 5y((3 * 7 + y * 7) + y(3 + y)) = 0 5y((21 + 7y) + y(3 + y)) = 0 5y(21 + 7y + (3 * y + y * y)) = 0 5y(21 + 7y + (3y + y2)) = 0 Combine like terms: 7y + 3y = 10y 5y(21 + 10y + y2) = 0 (21 * 5y + 10y * 5y + y2 * 5y) = 0 (105y + 50y2 + 5y3) = 0 Solving 105y + 50y2 + 5y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y'. 5y(21 + 10y + y2) = 0 Factor a trinomial. 5y((7 + y)(3 + y)) = 0 Ignore the factor 5.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 '(7 + y)' equal to zero and attempt to solve: Simplifying 7 + y = 0 Solving 7 + y = 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 + y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + y = 0 + -7 y = 0 + -7 Combine like terms: 0 + -7 = -7 y = -7 Simplifying y = -7Subproblem 3
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 = -3Solution
y = {0, -7, -3}
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