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Simplifying (3y + 2)(y + 3) = y + 14 Reorder the terms: (2 + 3y)(y + 3) = y + 14 Reorder the terms: (2 + 3y)(3 + y) = y + 14 Multiply (2 + 3y) * (3 + y) (2(3 + y) + 3y * (3 + y)) = y + 14 ((3 * 2 + y * 2) + 3y * (3 + y)) = y + 14 ((6 + 2y) + 3y * (3 + y)) = y + 14 (6 + 2y + (3 * 3y + y * 3y)) = y + 14 (6 + 2y + (9y + 3y2)) = y + 14 Combine like terms: 2y + 9y = 11y (6 + 11y + 3y2) = y + 14 Reorder the terms: 6 + 11y + 3y2 = 14 + y Solving 6 + 11y + 3y2 = 14 + y Solving for variable 'y'. Reorder the terms: 6 + -14 + 11y + -1y + 3y2 = 14 + y + -14 + -1y Combine like terms: 6 + -14 = -8 -8 + 11y + -1y + 3y2 = 14 + y + -14 + -1y Combine like terms: 11y + -1y = 10y -8 + 10y + 3y2 = 14 + y + -14 + -1y Reorder the terms: -8 + 10y + 3y2 = 14 + -14 + y + -1y Combine like terms: 14 + -14 = 0 -8 + 10y + 3y2 = 0 + y + -1y -8 + 10y + 3y2 = y + -1y Combine like terms: y + -1y = 0 -8 + 10y + 3y2 = 0 Factor a trinomial. (-4 + -1y)(2 + -3y) = 0Subproblem 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 + -3y)' equal to zero and attempt to solve: Simplifying 2 + -3y = 0 Solving 2 + -3y = 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 + -3y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3y = 0 + -2 -3y = 0 + -2 Combine like terms: 0 + -2 = -2 -3y = -2 Divide each side by '-3'. y = 0.6666666667 Simplifying y = 0.6666666667Solution
y = {-4, 0.6666666667}
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