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Simplifying (Y2 + -3y + -18)(3y + 15) = 0 Reorder the terms: (-18 + Y2 + -3y)(3y + 15) = 0 Reorder the terms: (-18 + Y2 + -3y)(15 + 3y) = 0 Multiply (-18 + Y2 + -3y) * (15 + 3y) (-18(15 + 3y) + Y2(15 + 3y) + -3y * (15 + 3y)) = 0 ((15 * -18 + 3y * -18) + Y2(15 + 3y) + -3y * (15 + 3y)) = 0 ((-270 + -54y) + Y2(15 + 3y) + -3y * (15 + 3y)) = 0 (-270 + -54y + (15 * Y2 + 3y * Y2) + -3y * (15 + 3y)) = 0 (-270 + -54y + (15Y2 + 3yY2) + -3y * (15 + 3y)) = 0 (-270 + -54y + 15Y2 + 3yY2 + (15 * -3y + 3y * -3y)) = 0 (-270 + -54y + 15Y2 + 3yY2 + (-45y + -9y2)) = 0 Reorder the terms: (-270 + 15Y2 + -54y + -45y + 3yY2 + -9y2) = 0 Combine like terms: -54y + -45y = -99y (-270 + 15Y2 + -99y + 3yY2 + -9y2) = 0 Solving -270 + 15Y2 + -99y + 3yY2 + -9y2 = 0 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '270' to each side of the equation. -270 + 15Y2 + -99y + 3yY2 + 270 + -9y2 = 0 + 270 Reorder the terms: -270 + 270 + 15Y2 + -99y + 3yY2 + -9y2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + 15Y2 + -99y + 3yY2 + -9y2 = 0 + 270 15Y2 + -99y + 3yY2 + -9y2 = 0 + 270 Combine like terms: 0 + 270 = 270 15Y2 + -99y + 3yY2 + -9y2 = 270 Add '99y' to each side of the equation. 15Y2 + -99y + 3yY2 + 99y + -9y2 = 270 + 99y Reorder the terms: 15Y2 + -99y + 99y + 3yY2 + -9y2 = 270 + 99y Combine like terms: -99y + 99y = 0 15Y2 + 0 + 3yY2 + -9y2 = 270 + 99y 15Y2 + 3yY2 + -9y2 = 270 + 99y Add '9y2' to each side of the equation. 15Y2 + 3yY2 + -9y2 + 9y2 = 270 + 99y + 9y2 Combine like terms: -9y2 + 9y2 = 0 15Y2 + 3yY2 + 0 = 270 + 99y + 9y2 15Y2 + 3yY2 = 270 + 99y + 9y2 Reorder the terms: -270 + 15Y2 + -99y + 3yY2 + -9y2 = 270 + 99y + 9y2 + -270 + -99y + -9y2 Reorder the terms: -270 + 15Y2 + -99y + 3yY2 + -9y2 = 270 + -270 + 99y + -99y + 9y2 + -9y2 Combine like terms: 270 + -270 = 0 -270 + 15Y2 + -99y + 3yY2 + -9y2 = 0 + 99y + -99y + 9y2 + -9y2 -270 + 15Y2 + -99y + 3yY2 + -9y2 = 99y + -99y + 9y2 + -9y2 Combine like terms: 99y + -99y = 0 -270 + 15Y2 + -99y + 3yY2 + -9y2 = 0 + 9y2 + -9y2 -270 + 15Y2 + -99y + 3yY2 + -9y2 = 9y2 + -9y2 Combine like terms: 9y2 + -9y2 = 0 -270 + 15Y2 + -99y + 3yY2 + -9y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-90 + 5Y2 + -33y + yY2 + -3y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-90 + 5Y2 + -33y + yY2 + -3y2)' equal to zero and attempt to solve: Simplifying -90 + 5Y2 + -33y + yY2 + -3y2 = 0 Solving -90 + 5Y2 + -33y + yY2 + -3y2 = 0 Move all terms containing Y to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 5Y2 + -33y + yY2 + 90 + -3y2 = 0 + 90 Reorder the terms: -90 + 90 + 5Y2 + -33y + yY2 + -3y2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 5Y2 + -33y + yY2 + -3y2 = 0 + 90 5Y2 + -33y + yY2 + -3y2 = 0 + 90 Combine like terms: 0 + 90 = 90 5Y2 + -33y + yY2 + -3y2 = 90 Add '33y' to each side of the equation. 5Y2 + -33y + yY2 + 33y + -3y2 = 90 + 33y Reorder the terms: 5Y2 + -33y + 33y + yY2 + -3y2 = 90 + 33y Combine like terms: -33y + 33y = 0 5Y2 + 0 + yY2 + -3y2 = 90 + 33y 5Y2 + yY2 + -3y2 = 90 + 33y Add '3y2' to each side of the equation. 5Y2 + yY2 + -3y2 + 3y2 = 90 + 33y + 3y2 Combine like terms: -3y2 + 3y2 = 0 5Y2 + yY2 + 0 = 90 + 33y + 3y2 5Y2 + yY2 = 90 + 33y + 3y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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