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Simplifying (4y + 7)(1 + y) = 0 Reorder the terms: (7 + 4y)(1 + y) = 0 Multiply (7 + 4y) * (1 + y) (7(1 + y) + 4y * (1 + y)) = 0 ((1 * 7 + y * 7) + 4y * (1 + y)) = 0 ((7 + 7y) + 4y * (1 + y)) = 0 (7 + 7y + (1 * 4y + y * 4y)) = 0 (7 + 7y + (4y + 4y2)) = 0 Combine like terms: 7y + 4y = 11y (7 + 11y + 4y2) = 0 Solving 7 + 11y + 4y2 = 0 Solving for variable 'y'. Factor a trinomial. (7 + 4y)(1 + y) = 0Subproblem 1
Set the factor '(7 + 4y)' equal to zero and attempt to solve: Simplifying 7 + 4y = 0 Solving 7 + 4y = 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 + 4y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4y = 0 + -7 4y = 0 + -7 Combine like terms: 0 + -7 = -7 4y = -7 Divide each side by '4'. y = -1.75 Simplifying y = -1.75Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 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 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Simplifying y = -1Solution
y = {-1.75, -1}
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