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Simplifying (5y + 2)(y + 4) = -3(5y + 2) Reorder the terms: (2 + 5y)(y + 4) = -3(5y + 2) Reorder the terms: (2 + 5y)(4 + y) = -3(5y + 2) Multiply (2 + 5y) * (4 + y) (2(4 + y) + 5y * (4 + y)) = -3(5y + 2) ((4 * 2 + y * 2) + 5y * (4 + y)) = -3(5y + 2) ((8 + 2y) + 5y * (4 + y)) = -3(5y + 2) (8 + 2y + (4 * 5y + y * 5y)) = -3(5y + 2) (8 + 2y + (20y + 5y2)) = -3(5y + 2) Combine like terms: 2y + 20y = 22y (8 + 22y + 5y2) = -3(5y + 2) Reorder the terms: 8 + 22y + 5y2 = -3(2 + 5y) 8 + 22y + 5y2 = (2 * -3 + 5y * -3) 8 + 22y + 5y2 = (-6 + -15y) Solving 8 + 22y + 5y2 = -6 + -15y Solving for variable 'y'. Reorder the terms: 8 + 6 + 22y + 15y + 5y2 = -6 + -15y + 6 + 15y Combine like terms: 8 + 6 = 14 14 + 22y + 15y + 5y2 = -6 + -15y + 6 + 15y Combine like terms: 22y + 15y = 37y 14 + 37y + 5y2 = -6 + -15y + 6 + 15y Reorder the terms: 14 + 37y + 5y2 = -6 + 6 + -15y + 15y Combine like terms: -6 + 6 = 0 14 + 37y + 5y2 = 0 + -15y + 15y 14 + 37y + 5y2 = -15y + 15y Combine like terms: -15y + 15y = 0 14 + 37y + 5y2 = 0 Factor a trinomial. (7 + y)(2 + 5y) = 0Subproblem 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 '(2 + 5y)' equal to zero and attempt to solve: Simplifying 2 + 5y = 0 Solving 2 + 5y = 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 + 5y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5y = 0 + -2 5y = 0 + -2 Combine like terms: 0 + -2 = -2 5y = -2 Divide each side by '5'. y = -0.4 Simplifying y = -0.4Solution
y = {-7, -0.4}
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