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Simplifying (4y + 12)(3y + 3) = 756 Reorder the terms: (12 + 4y)(3y + 3) = 756 Reorder the terms: (12 + 4y)(3 + 3y) = 756 Multiply (12 + 4y) * (3 + 3y) (12(3 + 3y) + 4y * (3 + 3y)) = 756 ((3 * 12 + 3y * 12) + 4y * (3 + 3y)) = 756 ((36 + 36y) + 4y * (3 + 3y)) = 756 (36 + 36y + (3 * 4y + 3y * 4y)) = 756 (36 + 36y + (12y + 12y2)) = 756 Combine like terms: 36y + 12y = 48y (36 + 48y + 12y2) = 756 Solving 36 + 48y + 12y2 = 756 Solving for variable 'y'. Reorder the terms: 36 + -756 + 48y + 12y2 = 756 + -756 Combine like terms: 36 + -756 = -720 -720 + 48y + 12y2 = 756 + -756 Combine like terms: 756 + -756 = 0 -720 + 48y + 12y2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-60 + 4y + y2) = 0 Factor a trinomial. 12((-10 + -1y)(6 + -1y)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-10 + -1y)' equal to zero and attempt to solve: Simplifying -10 + -1y = 0 Solving -10 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1y = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1y = 0 + 10 -1y = 0 + 10 Combine like terms: 0 + 10 = 10 -1y = 10 Divide each side by '-1'. y = -10 Simplifying y = -10Subproblem 2
Set the factor '(6 + -1y)' equal to zero and attempt to solve: Simplifying 6 + -1y = 0 Solving 6 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1y = 0 + -6 -1y = 0 + -6 Combine like terms: 0 + -6 = -6 -1y = -6 Divide each side by '-1'. y = 6 Simplifying y = 6Solution
y = {-10, 6}
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