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Simplifying 2y(5y + 6) = 16 Reorder the terms: 2y(6 + 5y) = 16 (6 * 2y + 5y * 2y) = 16 (12y + 10y2) = 16 Solving 12y + 10y2 = 16 Solving for variable 'y'. Reorder the terms: -16 + 12y + 10y2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 12y + 10y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 6y + 5y2) = 0 Factor a trinomial. 2((-2 + -1y)(4 + -5y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1y)' equal to zero and attempt to solve: Simplifying -2 + -1y = 0 Solving -2 + -1y = 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 + -1y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1y = 0 + 2 -1y = 0 + 2 Combine like terms: 0 + 2 = 2 -1y = 2 Divide each side by '-1'. y = -2 Simplifying y = -2Subproblem 2
Set the factor '(4 + -5y)' equal to zero and attempt to solve: Simplifying 4 + -5y = 0 Solving 4 + -5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5y = 0 + -4 -5y = 0 + -4 Combine like terms: 0 + -4 = -4 -5y = -4 Divide each side by '-5'. y = 0.8 Simplifying y = 0.8Solution
y = {-2, 0.8}
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