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Simplifying (3y + 6)(7y + 4) = 0 Reorder the terms: (6 + 3y)(7y + 4) = 0 Reorder the terms: (6 + 3y)(4 + 7y) = 0 Multiply (6 + 3y) * (4 + 7y) (6(4 + 7y) + 3y * (4 + 7y)) = 0 ((4 * 6 + 7y * 6) + 3y * (4 + 7y)) = 0 ((24 + 42y) + 3y * (4 + 7y)) = 0 (24 + 42y + (4 * 3y + 7y * 3y)) = 0 (24 + 42y + (12y + 21y2)) = 0 Combine like terms: 42y + 12y = 54y (24 + 54y + 21y2) = 0 Solving 24 + 54y + 21y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 18y + 7y2) = 0 Factor a trinomial. 3((2 + y)(4 + 7y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2Subproblem 2
Set the factor '(4 + 7y)' equal to zero and attempt to solve: Simplifying 4 + 7y = 0 Solving 4 + 7y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 7y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7y = 0 + -4 7y = 0 + -4 Combine like terms: 0 + -4 = -4 7y = -4 Divide each side by '7'. y = -0.5714285714 Simplifying y = -0.5714285714Solution
y = {-2, -0.5714285714}
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