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Simplifying (3y + 4)(y + 2) = 5(3y + 4) Reorder the terms: (4 + 3y)(y + 2) = 5(3y + 4) Reorder the terms: (4 + 3y)(2 + y) = 5(3y + 4) Multiply (4 + 3y) * (2 + y) (4(2 + y) + 3y * (2 + y)) = 5(3y + 4) ((2 * 4 + y * 4) + 3y * (2 + y)) = 5(3y + 4) ((8 + 4y) + 3y * (2 + y)) = 5(3y + 4) (8 + 4y + (2 * 3y + y * 3y)) = 5(3y + 4) (8 + 4y + (6y + 3y2)) = 5(3y + 4) Combine like terms: 4y + 6y = 10y (8 + 10y + 3y2) = 5(3y + 4) Reorder the terms: 8 + 10y + 3y2 = 5(4 + 3y) 8 + 10y + 3y2 = (4 * 5 + 3y * 5) 8 + 10y + 3y2 = (20 + 15y) Solving 8 + 10y + 3y2 = 20 + 15y Solving for variable 'y'. Reorder the terms: 8 + -20 + 10y + -15y + 3y2 = 20 + 15y + -20 + -15y Combine like terms: 8 + -20 = -12 -12 + 10y + -15y + 3y2 = 20 + 15y + -20 + -15y Combine like terms: 10y + -15y = -5y -12 + -5y + 3y2 = 20 + 15y + -20 + -15y Reorder the terms: -12 + -5y + 3y2 = 20 + -20 + 15y + -15y Combine like terms: 20 + -20 = 0 -12 + -5y + 3y2 = 0 + 15y + -15y -12 + -5y + 3y2 = 15y + -15y Combine like terms: 15y + -15y = 0 -12 + -5y + 3y2 = 0 Factor a trinomial. (-4 + -3y)(3 + -1y) = 0Subproblem 1
Set the factor '(-4 + -3y)' equal to zero and attempt to solve: Simplifying -4 + -3y = 0 Solving -4 + -3y = 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 + -3y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3y = 0 + 4 -3y = 0 + 4 Combine like terms: 0 + 4 = 4 -3y = 4 Divide each side by '-3'. y = -1.333333333 Simplifying y = -1.333333333Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve: Simplifying 3 + -1y = 0 Solving 3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y = 0 + -3 -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1y = -3 Divide each side by '-1'. y = 3 Simplifying y = 3Solution
y = {-1.333333333, 3}
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