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Simplifying (5y + 2)(8 + y) = 0 Reorder the terms: (2 + 5y)(8 + y) = 0 Multiply (2 + 5y) * (8 + y) (2(8 + y) + 5y * (8 + y)) = 0 ((8 * 2 + y * 2) + 5y * (8 + y)) = 0 ((16 + 2y) + 5y * (8 + y)) = 0 (16 + 2y + (8 * 5y + y * 5y)) = 0 (16 + 2y + (40y + 5y2)) = 0 Combine like terms: 2y + 40y = 42y (16 + 42y + 5y2) = 0 Solving 16 + 42y + 5y2 = 0 Solving for variable 'y'. Factor a trinomial. (8 + y)(2 + 5y) = 0Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve: Simplifying 8 + y = 0 Solving 8 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = 0 + -8 Combine like terms: 8 + -8 = 0 0 + y = 0 + -8 y = 0 + -8 Combine like terms: 0 + -8 = -8 y = -8 Simplifying y = -8Subproblem 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 = {-8, -0.4}
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