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Simplifying (2y + 3)(2y + 3) = cy2 + dy + 9 Reorder the terms: (3 + 2y)(2y + 3) = cy2 + dy + 9 Reorder the terms: (3 + 2y)(3 + 2y) = cy2 + dy + 9 Multiply (3 + 2y) * (3 + 2y) (3(3 + 2y) + 2y * (3 + 2y)) = cy2 + dy + 9 ((3 * 3 + 2y * 3) + 2y * (3 + 2y)) = cy2 + dy + 9 ((9 + 6y) + 2y * (3 + 2y)) = cy2 + dy + 9 (9 + 6y + (3 * 2y + 2y * 2y)) = cy2 + dy + 9 (9 + 6y + (6y + 4y2)) = cy2 + dy + 9 Combine like terms: 6y + 6y = 12y (9 + 12y + 4y2) = cy2 + dy + 9 Reorder the terms: 9 + 12y + 4y2 = 9 + cy2 + dy Add '-9' to each side of the equation. 9 + 12y + -9 + 4y2 = 9 + cy2 + -9 + dy Reorder the terms: 9 + -9 + 12y + 4y2 = 9 + cy2 + -9 + dy Combine like terms: 9 + -9 = 0 0 + 12y + 4y2 = 9 + cy2 + -9 + dy 12y + 4y2 = 9 + cy2 + -9 + dy Reorder the terms: 12y + 4y2 = 9 + -9 + cy2 + dy Combine like terms: 9 + -9 = 0 12y + 4y2 = 0 + cy2 + dy 12y + 4y2 = cy2 + dy Solving 12y + 4y2 = cy2 + dy Solving for variable 'y'. Reorder the terms: -1cy2 + -1dy + 12y + 4y2 = cy2 + dy + -1cy2 + -1dy Reorder the terms: -1cy2 + -1dy + 12y + 4y2 = cy2 + -1cy2 + dy + -1dy Combine like terms: cy2 + -1cy2 = 0 -1cy2 + -1dy + 12y + 4y2 = 0 + dy + -1dy -1cy2 + -1dy + 12y + 4y2 = dy + -1dy Combine like terms: dy + -1dy = 0 -1cy2 + -1dy + 12y + 4y2 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-1cy + -1d + 12 + 4y) = 0Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(-1cy + -1d + 12 + 4y)' equal to zero and attempt to solve: Simplifying -1cy + -1d + 12 + 4y = 0 Reorder the terms: 12 + -1cy + -1d + 4y = 0 Solving 12 + -1cy + -1d + 4y = 0 Move all terms containing y to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -1cy + -1d + -12 + 4y = 0 + -12 Reorder the terms: 12 + -12 + -1cy + -1d + 4y = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1cy + -1d + 4y = 0 + -12 -1cy + -1d + 4y = 0 + -12 Combine like terms: 0 + -12 = -12 -1cy + -1d + 4y = -12 Add 'd' to each side of the equation. -1cy + -1d + d + 4y = -12 + d Combine like terms: -1d + d = 0 -1cy + 0 + 4y = -12 + d -1cy + 4y = -12 + d The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
y = {0}
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