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Simplifying (3y + 3)(3y + 3) = 81 Reorder the terms: (3 + 3y)(3y + 3) = 81 Reorder the terms: (3 + 3y)(3 + 3y) = 81 Multiply (3 + 3y) * (3 + 3y) (3(3 + 3y) + 3y * (3 + 3y)) = 81 ((3 * 3 + 3y * 3) + 3y * (3 + 3y)) = 81 ((9 + 9y) + 3y * (3 + 3y)) = 81 (9 + 9y + (3 * 3y + 3y * 3y)) = 81 (9 + 9y + (9y + 9y2)) = 81 Combine like terms: 9y + 9y = 18y (9 + 18y + 9y2) = 81 Solving 9 + 18y + 9y2 = 81 Solving for variable 'y'. Reorder the terms: 9 + -81 + 18y + 9y2 = 81 + -81 Combine like terms: 9 + -81 = -72 -72 + 18y + 9y2 = 81 + -81 Combine like terms: 81 + -81 = 0 -72 + 18y + 9y2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-8 + 2y + y2) = 0 Factor a trinomial. 9((-4 + -1y)(2 + -1y)) = 0 Ignore the factor 9.Subproblem 1
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 = -4Subproblem 2
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 = 2Solution
y = {-4, 2}
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