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Simplifying 3Y2 + 3Y + 21Y + 21 = 0 Reorder the terms: 21 + 3Y + 21Y + 3Y2 = 0 Combine like terms: 3Y + 21Y = 24Y 21 + 24Y + 3Y2 = 0 Solving 21 + 24Y + 3Y2 = 0 Solving for variable 'Y'. Factor out the Greatest Common Factor (GCF), '3'. 3(7 + 8Y + Y2) = 0 Factor a trinomial. 3((7 + Y)(1 + Y)) = 0 Ignore the factor 3.Subproblem 1
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 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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