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Simplifying (5y + 11)(14y + 7) + -1(15y + 8)(5y + 11) = 0 Reorder the terms: (11 + 5y)(14y + 7) + -1(15y + 8)(5y + 11) = 0 Reorder the terms: (11 + 5y)(7 + 14y) + -1(15y + 8)(5y + 11) = 0 Multiply (11 + 5y) * (7 + 14y) (11(7 + 14y) + 5y * (7 + 14y)) + -1(15y + 8)(5y + 11) = 0 ((7 * 11 + 14y * 11) + 5y * (7 + 14y)) + -1(15y + 8)(5y + 11) = 0 ((77 + 154y) + 5y * (7 + 14y)) + -1(15y + 8)(5y + 11) = 0 (77 + 154y + (7 * 5y + 14y * 5y)) + -1(15y + 8)(5y + 11) = 0 (77 + 154y + (35y + 70y2)) + -1(15y + 8)(5y + 11) = 0 Combine like terms: 154y + 35y = 189y (77 + 189y + 70y2) + -1(15y + 8)(5y + 11) = 0 Reorder the terms: 77 + 189y + 70y2 + -1(8 + 15y)(5y + 11) = 0 Reorder the terms: 77 + 189y + 70y2 + -1(8 + 15y)(11 + 5y) = 0 Multiply (8 + 15y) * (11 + 5y) 77 + 189y + 70y2 + -1(8(11 + 5y) + 15y * (11 + 5y)) = 0 77 + 189y + 70y2 + -1((11 * 8 + 5y * 8) + 15y * (11 + 5y)) = 0 77 + 189y + 70y2 + -1((88 + 40y) + 15y * (11 + 5y)) = 0 77 + 189y + 70y2 + -1(88 + 40y + (11 * 15y + 5y * 15y)) = 0 77 + 189y + 70y2 + -1(88 + 40y + (165y + 75y2)) = 0 Combine like terms: 40y + 165y = 205y 77 + 189y + 70y2 + -1(88 + 205y + 75y2) = 0 77 + 189y + 70y2 + (88 * -1 + 205y * -1 + 75y2 * -1) = 0 77 + 189y + 70y2 + (-88 + -205y + -75y2) = 0 Reorder the terms: 77 + -88 + 189y + -205y + 70y2 + -75y2 = 0 Combine like terms: 77 + -88 = -11 -11 + 189y + -205y + 70y2 + -75y2 = 0 Combine like terms: 189y + -205y = -16y -11 + -16y + 70y2 + -75y2 = 0 Combine like terms: 70y2 + -75y2 = -5y2 -11 + -16y + -5y2 = 0 Solving -11 + -16y + -5y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 16y + 5y2) = 0 Factor a trinomial. -1((11 + 5y)(1 + y)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 5y)' equal to zero and attempt to solve: Simplifying 11 + 5y = 0 Solving 11 + 5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 5y = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 5y = 0 + -11 5y = 0 + -11 Combine like terms: 0 + -11 = -11 5y = -11 Divide each side by '5'. y = -2.2 Simplifying y = -2.2Subproblem 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 = {-2.2, -1}
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