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Simplifying (2y + 1)(3y) = 108 Reorder the terms: (1 + 2y)(3y) = 108 Remove parenthesis around (3y) (1 + 2y) * 3y = 108 Reorder the terms for easier multiplication: 3y(1 + 2y) = 108 (1 * 3y + 2y * 3y) = 108 (3y + 6y2) = 108 Solving 3y + 6y2 = 108 Solving for variable 'y'. Reorder the terms: -108 + 3y + 6y2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + 3y + 6y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-36 + y + 2y2) = 0 Factor a trinomial. 3((-9 + -2y)(4 + -1y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + -2y)' equal to zero and attempt to solve: Simplifying -9 + -2y = 0 Solving -9 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2y = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2y = 0 + 9 -2y = 0 + 9 Combine like terms: 0 + 9 = 9 -2y = 9 Divide each side by '-2'. y = -4.5 Simplifying y = -4.5Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 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 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4Solution
y = {-4.5, 4}
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