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Simplifying (-11y + 3)(15y + -5) + -1(-6y + -12)(-11y + 3) = 0 Reorder the terms: (3 + -11y)(15y + -5) + -1(-6y + -12)(-11y + 3) = 0 Reorder the terms: (3 + -11y)(-5 + 15y) + -1(-6y + -12)(-11y + 3) = 0 Multiply (3 + -11y) * (-5 + 15y) (3(-5 + 15y) + -11y * (-5 + 15y)) + -1(-6y + -12)(-11y + 3) = 0 ((-5 * 3 + 15y * 3) + -11y * (-5 + 15y)) + -1(-6y + -12)(-11y + 3) = 0 ((-15 + 45y) + -11y * (-5 + 15y)) + -1(-6y + -12)(-11y + 3) = 0 (-15 + 45y + (-5 * -11y + 15y * -11y)) + -1(-6y + -12)(-11y + 3) = 0 (-15 + 45y + (55y + -165y2)) + -1(-6y + -12)(-11y + 3) = 0 Combine like terms: 45y + 55y = 100y (-15 + 100y + -165y2) + -1(-6y + -12)(-11y + 3) = 0 Reorder the terms: -15 + 100y + -165y2 + -1(-12 + -6y)(-11y + 3) = 0 Reorder the terms: -15 + 100y + -165y2 + -1(-12 + -6y)(3 + -11y) = 0 Multiply (-12 + -6y) * (3 + -11y) -15 + 100y + -165y2 + -1(-12(3 + -11y) + -6y * (3 + -11y)) = 0 -15 + 100y + -165y2 + -1((3 * -12 + -11y * -12) + -6y * (3 + -11y)) = 0 -15 + 100y + -165y2 + -1((-36 + 132y) + -6y * (3 + -11y)) = 0 -15 + 100y + -165y2 + -1(-36 + 132y + (3 * -6y + -11y * -6y)) = 0 -15 + 100y + -165y2 + -1(-36 + 132y + (-18y + 66y2)) = 0 Combine like terms: 132y + -18y = 114y -15 + 100y + -165y2 + -1(-36 + 114y + 66y2) = 0 -15 + 100y + -165y2 + (-36 * -1 + 114y * -1 + 66y2 * -1) = 0 -15 + 100y + -165y2 + (36 + -114y + -66y2) = 0 Reorder the terms: -15 + 36 + 100y + -114y + -165y2 + -66y2 = 0 Combine like terms: -15 + 36 = 21 21 + 100y + -114y + -165y2 + -66y2 = 0 Combine like terms: 100y + -114y = -14y 21 + -14y + -165y2 + -66y2 = 0 Combine like terms: -165y2 + -66y2 = -231y2 21 + -14y + -231y2 = 0 Solving 21 + -14y + -231y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '7'. 7(3 + -2y + -33y2) = 0 Factor a trinomial. 7((3 + -11y)(1 + 3y)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(3 + -11y)' equal to zero and attempt to solve: Simplifying 3 + -11y = 0 Solving 3 + -11y = 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 + -11y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -11y = 0 + -3 -11y = 0 + -3 Combine like terms: 0 + -3 = -3 -11y = -3 Divide each side by '-11'. y = 0.2727272727 Simplifying y = 0.2727272727Subproblem 2
Set the factor '(1 + 3y)' equal to zero and attempt to solve: Simplifying 1 + 3y = 0 Solving 1 + 3y = 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 + 3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3y = 0 + -1 3y = 0 + -1 Combine like terms: 0 + -1 = -1 3y = -1 Divide each side by '3'. y = -0.3333333333 Simplifying y = -0.3333333333Solution
y = {0.2727272727, -0.3333333333}
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