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Simplifying (14y + 10)(13y + 6) + -1(5y + 2)(14y + 10) = 0 Reorder the terms: (10 + 14y)(13y + 6) + -1(5y + 2)(14y + 10) = 0 Reorder the terms: (10 + 14y)(6 + 13y) + -1(5y + 2)(14y + 10) = 0 Multiply (10 + 14y) * (6 + 13y) (10(6 + 13y) + 14y * (6 + 13y)) + -1(5y + 2)(14y + 10) = 0 ((6 * 10 + 13y * 10) + 14y * (6 + 13y)) + -1(5y + 2)(14y + 10) = 0 ((60 + 130y) + 14y * (6 + 13y)) + -1(5y + 2)(14y + 10) = 0 (60 + 130y + (6 * 14y + 13y * 14y)) + -1(5y + 2)(14y + 10) = 0 (60 + 130y + (84y + 182y2)) + -1(5y + 2)(14y + 10) = 0 Combine like terms: 130y + 84y = 214y (60 + 214y + 182y2) + -1(5y + 2)(14y + 10) = 0 Reorder the terms: 60 + 214y + 182y2 + -1(2 + 5y)(14y + 10) = 0 Reorder the terms: 60 + 214y + 182y2 + -1(2 + 5y)(10 + 14y) = 0 Multiply (2 + 5y) * (10 + 14y) 60 + 214y + 182y2 + -1(2(10 + 14y) + 5y * (10 + 14y)) = 0 60 + 214y + 182y2 + -1((10 * 2 + 14y * 2) + 5y * (10 + 14y)) = 0 60 + 214y + 182y2 + -1((20 + 28y) + 5y * (10 + 14y)) = 0 60 + 214y + 182y2 + -1(20 + 28y + (10 * 5y + 14y * 5y)) = 0 60 + 214y + 182y2 + -1(20 + 28y + (50y + 70y2)) = 0 Combine like terms: 28y + 50y = 78y 60 + 214y + 182y2 + -1(20 + 78y + 70y2) = 0 60 + 214y + 182y2 + (20 * -1 + 78y * -1 + 70y2 * -1) = 0 60 + 214y + 182y2 + (-20 + -78y + -70y2) = 0 Reorder the terms: 60 + -20 + 214y + -78y + 182y2 + -70y2 = 0 Combine like terms: 60 + -20 = 40 40 + 214y + -78y + 182y2 + -70y2 = 0 Combine like terms: 214y + -78y = 136y 40 + 136y + 182y2 + -70y2 = 0 Combine like terms: 182y2 + -70y2 = 112y2 40 + 136y + 112y2 = 0 Solving 40 + 136y + 112y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '8'. 8(5 + 17y + 14y2) = 0 Factor a trinomial. 8((5 + 7y)(1 + 2y)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(5 + 7y)' equal to zero and attempt to solve: Simplifying 5 + 7y = 0 Solving 5 + 7y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 7y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7y = 0 + -5 7y = 0 + -5 Combine like terms: 0 + -5 = -5 7y = -5 Divide each side by '7'. y = -0.7142857143 Simplifying y = -0.7142857143Subproblem 2
Set the factor '(1 + 2y)' equal to zero and attempt to solve: Simplifying 1 + 2y = 0 Solving 1 + 2y = 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 + 2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2y = 0 + -1 2y = 0 + -1 Combine like terms: 0 + -1 = -1 2y = -1 Divide each side by '2'. y = -0.5 Simplifying y = -0.5Solution
y = {-0.7142857143, -0.5}
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