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Simplifying 5(y + 1)(-1y + 7) = 0 Reorder the terms: 5(1 + y)(-1y + 7) = 0 Reorder the terms: 5(1 + y)(7 + -1y) = 0 Multiply (1 + y) * (7 + -1y) 5(1(7 + -1y) + y(7 + -1y)) = 0 5((7 * 1 + -1y * 1) + y(7 + -1y)) = 0 5((7 + -1y) + y(7 + -1y)) = 0 5(7 + -1y + (7 * y + -1y * y)) = 0 5(7 + -1y + (7y + -1y2)) = 0 Combine like terms: -1y + 7y = 6y 5(7 + 6y + -1y2) = 0 (7 * 5 + 6y * 5 + -1y2 * 5) = 0 (35 + 30y + -5y2) = 0 Solving 35 + 30y + -5y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5'. 5(7 + 6y + -1y2) = 0 Factor a trinomial. 5((7 + -1y)(1 + y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7 + -1y)' equal to zero and attempt to solve: Simplifying 7 + -1y = 0 Solving 7 + -1y = 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 + -1y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1y = 0 + -7 -1y = 0 + -7 Combine like terms: 0 + -7 = -7 -1y = -7 Divide each side by '-1'. y = 7 Simplifying y = 7Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Simplifying y = -1Solution
y = {7, -1}
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