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Simplifying 6y(y + 2) = 18 Reorder the terms: 6y(2 + y) = 18 (2 * 6y + y * 6y) = 18 (12y + 6y2) = 18 Solving 12y + 6y2 = 18 Solving for variable 'y'. Reorder the terms: -18 + 12y + 6y2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 12y + 6y2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + 2y + y2) = 0 Factor a trinomial. 6((-3 + -1y)(1 + -1y)) = 0 Ignore the factor 6.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 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 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 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1Solution
y = {-3, 1}
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