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Simplifying (3y + 11)(2y + 23) = 0 Reorder the terms: (11 + 3y)(2y + 23) = 0 Reorder the terms: (11 + 3y)(23 + 2y) = 0 Multiply (11 + 3y) * (23 + 2y) (11(23 + 2y) + 3y * (23 + 2y)) = 0 ((23 * 11 + 2y * 11) + 3y * (23 + 2y)) = 0 ((253 + 22y) + 3y * (23 + 2y)) = 0 (253 + 22y + (23 * 3y + 2y * 3y)) = 0 (253 + 22y + (69y + 6y2)) = 0 Combine like terms: 22y + 69y = 91y (253 + 91y + 6y2) = 0 Solving 253 + 91y + 6y2 = 0 Solving for variable 'y'. Factor a trinomial. (23 + 2y)(11 + 3y) = 0Subproblem 1
Set the factor '(23 + 2y)' equal to zero and attempt to solve: Simplifying 23 + 2y = 0 Solving 23 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + 2y = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 2y = 0 + -23 2y = 0 + -23 Combine like terms: 0 + -23 = -23 2y = -23 Divide each side by '2'. y = -11.5 Simplifying y = -11.5Subproblem 2
Set the factor '(11 + 3y)' equal to zero and attempt to solve: Simplifying 11 + 3y = 0 Solving 11 + 3y = 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 + 3y = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 3y = 0 + -11 3y = 0 + -11 Combine like terms: 0 + -11 = -11 3y = -11 Divide each side by '3'. y = -3.666666667 Simplifying y = -3.666666667Solution
y = {-11.5, -3.666666667}
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