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Simplifying (3y + 2)(y + 3) = -2(3y + 2) Reorder the terms: (2 + 3y)(y + 3) = -2(3y + 2) Reorder the terms: (2 + 3y)(3 + y) = -2(3y + 2) Multiply (2 + 3y) * (3 + y) (2(3 + y) + 3y * (3 + y)) = -2(3y + 2) ((3 * 2 + y * 2) + 3y * (3 + y)) = -2(3y + 2) ((6 + 2y) + 3y * (3 + y)) = -2(3y + 2) (6 + 2y + (3 * 3y + y * 3y)) = -2(3y + 2) (6 + 2y + (9y + 3y2)) = -2(3y + 2) Combine like terms: 2y + 9y = 11y (6 + 11y + 3y2) = -2(3y + 2) Reorder the terms: 6 + 11y + 3y2 = -2(2 + 3y) 6 + 11y + 3y2 = (2 * -2 + 3y * -2) 6 + 11y + 3y2 = (-4 + -6y) Solving 6 + 11y + 3y2 = -4 + -6y Solving for variable 'y'. Reorder the terms: 6 + 4 + 11y + 6y + 3y2 = -4 + -6y + 4 + 6y Combine like terms: 6 + 4 = 10 10 + 11y + 6y + 3y2 = -4 + -6y + 4 + 6y Combine like terms: 11y + 6y = 17y 10 + 17y + 3y2 = -4 + -6y + 4 + 6y Reorder the terms: 10 + 17y + 3y2 = -4 + 4 + -6y + 6y Combine like terms: -4 + 4 = 0 10 + 17y + 3y2 = 0 + -6y + 6y 10 + 17y + 3y2 = -6y + 6y Combine like terms: -6y + 6y = 0 10 + 17y + 3y2 = 0 Factor a trinomial. (5 + y)(2 + 3y) = 0Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve: Simplifying 5 + y = 0 Solving 5 + y = 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 + y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0 + -5 y = 0 + -5 Combine like terms: 0 + -5 = -5 y = -5 Simplifying y = -5Subproblem 2
Set the factor '(2 + 3y)' equal to zero and attempt to solve: Simplifying 2 + 3y = 0 Solving 2 + 3y = 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 + 3y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3y = 0 + -2 3y = 0 + -2 Combine like terms: 0 + -2 = -2 3y = -2 Divide each side by '3'. y = -0.6666666667 Simplifying y = -0.6666666667Solution
y = {-5, -0.6666666667}
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