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Simplifying 3(7 + y)(1 + 3y) = 0 Multiply (7 + y) * (1 + 3y) 3(7(1 + 3y) + y(1 + 3y)) = 0 3((1 * 7 + 3y * 7) + y(1 + 3y)) = 0 3((7 + 21y) + y(1 + 3y)) = 0 3(7 + 21y + (1 * y + 3y * y)) = 0 3(7 + 21y + (1y + 3y2)) = 0 Combine like terms: 21y + 1y = 22y 3(7 + 22y + 3y2) = 0 (7 * 3 + 22y * 3 + 3y2 * 3) = 0 (21 + 66y + 9y2) = 0 Solving 21 + 66y + 9y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(7 + 22y + 3y2) = 0 Factor a trinomial. 3((7 + y)(1 + 3y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve: Simplifying 7 + y = 0 Solving 7 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + y = 0 + -7 y = 0 + -7 Combine like terms: 0 + -7 = -7 y = -7 Simplifying y = -7Subproblem 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 = {-7, -0.3333333333}
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