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Simplifying 3y(y + 1) = -1(6y + 4) + y Reorder the terms: 3y(1 + y) = -1(6y + 4) + y (1 * 3y + y * 3y) = -1(6y + 4) + y (3y + 3y2) = -1(6y + 4) + y Reorder the terms: 3y + 3y2 = -1(4 + 6y) + y 3y + 3y2 = (4 * -1 + 6y * -1) + y 3y + 3y2 = (-4 + -6y) + y Combine like terms: -6y + y = -5y 3y + 3y2 = -4 + -5y Solving 3y + 3y2 = -4 + -5y Solving for variable 'y'. Reorder the terms: 4 + 3y + 5y + 3y2 = -4 + -5y + 4 + 5y Combine like terms: 3y + 5y = 8y 4 + 8y + 3y2 = -4 + -5y + 4 + 5y Reorder the terms: 4 + 8y + 3y2 = -4 + 4 + -5y + 5y Combine like terms: -4 + 4 = 0 4 + 8y + 3y2 = 0 + -5y + 5y 4 + 8y + 3y2 = -5y + 5y Combine like terms: -5y + 5y = 0 4 + 8y + 3y2 = 0 Factor a trinomial. (2 + y)(2 + 3y) = 0Subproblem 1
Set the factor '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 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 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2Subproblem 2
Set the factor '(2 + 3y)' equal to zero and attempt to solve: Simplifying 2 + 3y = 0 Solving 2 + 3y = 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 + 3y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3y = 0 + -2 3y = 0 + -2 Combine like terms: 0 + -2 = -2 3y = -2 Divide each side by '3'. y = -0.6666666667 Simplifying y = -0.6666666667Solution
y = {-2, -0.6666666667}
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