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Simplifying (3y2 + -8) + (5y + 9) + -1(y2 + -6y + -4) = 0 Reorder the terms: (-8 + 3y2) + (5y + 9) + -1(y2 + -6y + -4) = 0 Remove parenthesis around (-8 + 3y2) -8 + 3y2 + (5y + 9) + -1(y2 + -6y + -4) = 0 Reorder the terms: -8 + 3y2 + (9 + 5y) + -1(y2 + -6y + -4) = 0 Remove parenthesis around (9 + 5y) -8 + 3y2 + 9 + 5y + -1(y2 + -6y + -4) = 0 Reorder the terms: -8 + 3y2 + 9 + 5y + -1(-4 + -6y + y2) = 0 -8 + 3y2 + 9 + 5y + (-4 * -1 + -6y * -1 + y2 * -1) = 0 -8 + 3y2 + 9 + 5y + (4 + 6y + -1y2) = 0 Reorder the terms: -8 + 9 + 4 + 5y + 6y + 3y2 + -1y2 = 0 Combine like terms: -8 + 9 = 1 1 + 4 + 5y + 6y + 3y2 + -1y2 = 0 Combine like terms: 1 + 4 = 5 5 + 5y + 6y + 3y2 + -1y2 = 0 Combine like terms: 5y + 6y = 11y 5 + 11y + 3y2 + -1y2 = 0 Combine like terms: 3y2 + -1y2 = 2y2 5 + 11y + 2y2 = 0 Solving 5 + 11y + 2y2 = 0 Solving for variable 'y'. Factor a trinomial. (5 + y)(1 + 2y) = 0Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve: Simplifying 5 + y = 0 Solving 5 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0 + -5 y = 0 + -5 Combine like terms: 0 + -5 = -5 y = -5 Simplifying y = -5Subproblem 2
Set the factor '(1 + 2y)' equal to zero and attempt to solve: Simplifying 1 + 2y = 0 Solving 1 + 2y = 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 + 2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2y = 0 + -1 2y = 0 + -1 Combine like terms: 0 + -1 = -1 2y = -1 Divide each side by '2'. y = -0.5 Simplifying y = -0.5Solution
y = {-5, -0.5}
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