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Simplifying (6y + -1y + 5) + (-4y2 + 3y + 7) = 0 Reorder the terms: (5 + 6y + -1y) + (-4y2 + 3y + 7) = 0 Combine like terms: 6y + -1y = 5y (5 + 5y) + (-4y2 + 3y + 7) = 0 Remove parenthesis around (5 + 5y) 5 + 5y + (-4y2 + 3y + 7) = 0 Reorder the terms: 5 + 5y + (7 + 3y + -4y2) = 0 Remove parenthesis around (7 + 3y + -4y2) 5 + 5y + 7 + 3y + -4y2 = 0 Reorder the terms: 5 + 7 + 5y + 3y + -4y2 = 0 Combine like terms: 5 + 7 = 12 12 + 5y + 3y + -4y2 = 0 Combine like terms: 5y + 3y = 8y 12 + 8y + -4y2 = 0 Solving 12 + 8y + -4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + 2y + -1y2) = 0 Factor a trinomial. 4((3 + -1y)(1 + y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -1y)' equal to zero and attempt to solve: Simplifying 3 + -1y = 0 Solving 3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y = 0 + -3 -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1y = -3 Divide each side by '-1'. y = 3 Simplifying y = 3Subproblem 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 = {3, -1}
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