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Simplifying (4y + 3)(y + 6) = -4(4y + 3) Reorder the terms: (3 + 4y)(y + 6) = -4(4y + 3) Reorder the terms: (3 + 4y)(6 + y) = -4(4y + 3) Multiply (3 + 4y) * (6 + y) (3(6 + y) + 4y * (6 + y)) = -4(4y + 3) ((6 * 3 + y * 3) + 4y * (6 + y)) = -4(4y + 3) ((18 + 3y) + 4y * (6 + y)) = -4(4y + 3) (18 + 3y + (6 * 4y + y * 4y)) = -4(4y + 3) (18 + 3y + (24y + 4y2)) = -4(4y + 3) Combine like terms: 3y + 24y = 27y (18 + 27y + 4y2) = -4(4y + 3) Reorder the terms: 18 + 27y + 4y2 = -4(3 + 4y) 18 + 27y + 4y2 = (3 * -4 + 4y * -4) 18 + 27y + 4y2 = (-12 + -16y) Solving 18 + 27y + 4y2 = -12 + -16y Solving for variable 'y'. Reorder the terms: 18 + 12 + 27y + 16y + 4y2 = -12 + -16y + 12 + 16y Combine like terms: 18 + 12 = 30 30 + 27y + 16y + 4y2 = -12 + -16y + 12 + 16y Combine like terms: 27y + 16y = 43y 30 + 43y + 4y2 = -12 + -16y + 12 + 16y Reorder the terms: 30 + 43y + 4y2 = -12 + 12 + -16y + 16y Combine like terms: -12 + 12 = 0 30 + 43y + 4y2 = 0 + -16y + 16y 30 + 43y + 4y2 = -16y + 16y Combine like terms: -16y + 16y = 0 30 + 43y + 4y2 = 0 Factor a trinomial. (10 + y)(3 + 4y) = 0Subproblem 1
Set the factor '(10 + y)' equal to zero and attempt to solve: Simplifying 10 + y = 0 Solving 10 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + y = 0 + -10 Combine like terms: 10 + -10 = 0 0 + y = 0 + -10 y = 0 + -10 Combine like terms: 0 + -10 = -10 y = -10 Simplifying y = -10Subproblem 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 = {-10, -0.75}
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