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Simplifying (4y + 3)(y + 2) = -3(4y + 3) Reorder the terms: (3 + 4y)(y + 2) = -3(4y + 3) Reorder the terms: (3 + 4y)(2 + y) = -3(4y + 3) Multiply (3 + 4y) * (2 + y) (3(2 + y) + 4y * (2 + y)) = -3(4y + 3) ((2 * 3 + y * 3) + 4y * (2 + y)) = -3(4y + 3) ((6 + 3y) + 4y * (2 + y)) = -3(4y + 3) (6 + 3y + (2 * 4y + y * 4y)) = -3(4y + 3) (6 + 3y + (8y + 4y2)) = -3(4y + 3) Combine like terms: 3y + 8y = 11y (6 + 11y + 4y2) = -3(4y + 3) Reorder the terms: 6 + 11y + 4y2 = -3(3 + 4y) 6 + 11y + 4y2 = (3 * -3 + 4y * -3) 6 + 11y + 4y2 = (-9 + -12y) Solving 6 + 11y + 4y2 = -9 + -12y Solving for variable 'y'. Reorder the terms: 6 + 9 + 11y + 12y + 4y2 = -9 + -12y + 9 + 12y Combine like terms: 6 + 9 = 15 15 + 11y + 12y + 4y2 = -9 + -12y + 9 + 12y Combine like terms: 11y + 12y = 23y 15 + 23y + 4y2 = -9 + -12y + 9 + 12y Reorder the terms: 15 + 23y + 4y2 = -9 + 9 + -12y + 12y Combine like terms: -9 + 9 = 0 15 + 23y + 4y2 = 0 + -12y + 12y 15 + 23y + 4y2 = -12y + 12y Combine like terms: -12y + 12y = 0 15 + 23y + 4y2 = 0 Factor a trinomial. (5 + y)(3 + 4y) = 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 '(3 + 4y)' equal to zero and attempt to solve: Simplifying 3 + 4y = 0 Solving 3 + 4y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4y = 0 + -3 4y = 0 + -3 Combine like terms: 0 + -3 = -3 4y = -3 Divide each side by '4'. y = -0.75 Simplifying y = -0.75Solution
y = {-5, -0.75}
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