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Simplifying 0 = 6y2 + 31y + 5 Reorder the terms: 0 = 5 + 31y + 6y2 Solving 0 = 5 + 31y + 6y2 Solving for variable 'y'. Combine like terms: 0 + -5 = -5 -5 + -31y + -6y2 = 5 + 31y + 6y2 + -5 + -31y + -6y2 Reorder the terms: -5 + -31y + -6y2 = 5 + -5 + 31y + -31y + 6y2 + -6y2 Combine like terms: 5 + -5 = 0 -5 + -31y + -6y2 = 0 + 31y + -31y + 6y2 + -6y2 -5 + -31y + -6y2 = 31y + -31y + 6y2 + -6y2 Combine like terms: 31y + -31y = 0 -5 + -31y + -6y2 = 0 + 6y2 + -6y2 -5 + -31y + -6y2 = 6y2 + -6y2 Combine like terms: 6y2 + -6y2 = 0 -5 + -31y + -6y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 31y + 6y2) = 0 Factor a trinomial. -1((5 + y)(1 + 6y)) = 0 Ignore the factor -1.Subproblem 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 + 6y)' equal to zero and attempt to solve: Simplifying 1 + 6y = 0 Solving 1 + 6y = 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 + 6y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6y = 0 + -1 6y = 0 + -1 Combine like terms: 0 + -1 = -1 6y = -1 Divide each side by '6'. y = -0.1666666667 Simplifying y = -0.1666666667Solution
y = {-5, -0.1666666667}
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