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Simplifying (4y + 1)(4 + y) = 0 Reorder the terms: (1 + 4y)(4 + y) = 0 Multiply (1 + 4y) * (4 + y) (1(4 + y) + 4y * (4 + y)) = 0 ((4 * 1 + y * 1) + 4y * (4 + y)) = 0 ((4 + 1y) + 4y * (4 + y)) = 0 (4 + 1y + (4 * 4y + y * 4y)) = 0 (4 + 1y + (16y + 4y2)) = 0 Combine like terms: 1y + 16y = 17y (4 + 17y + 4y2) = 0 Solving 4 + 17y + 4y2 = 0 Solving for variable 'y'. Factor a trinomial. (4 + y)(1 + 4y) = 0Subproblem 1
Set the factor '(4 + y)' equal to zero and attempt to solve: Simplifying 4 + y = 0 Solving 4 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + y = 0 + -4 y = 0 + -4 Combine like terms: 0 + -4 = -4 y = -4 Simplifying y = -4Subproblem 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 = {-4, -0.25}
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