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Simplifying (7 + y)(4y + 1) = 0 Reorder the terms: (7 + y)(1 + 4y) = 0 Multiply (7 + y) * (1 + 4y) (7(1 + 4y) + y(1 + 4y)) = 0 ((1 * 7 + 4y * 7) + y(1 + 4y)) = 0 ((7 + 28y) + y(1 + 4y)) = 0 (7 + 28y + (1 * y + 4y * y)) = 0 (7 + 28y + (1y + 4y2)) = 0 Combine like terms: 28y + 1y = 29y (7 + 29y + 4y2) = 0 Solving 7 + 29y + 4y2 = 0 Solving for variable 'y'. Factor a trinomial. (7 + y)(1 + 4y) = 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 '(1 + 4y)' equal to zero and attempt to solve: Simplifying 1 + 4y = 0 Solving 1 + 4y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4y = 0 + -1 4y = 0 + -1 Combine like terms: 0 + -1 = -1 4y = -1 Divide each side by '4'. y = -0.25 Simplifying y = -0.25Solution
y = {-7, -0.25}
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