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Simplifying (3y + 2)(5y + 4) = 0 Reorder the terms: (2 + 3y)(5y + 4) = 0 Reorder the terms: (2 + 3y)(4 + 5y) = 0 Multiply (2 + 3y) * (4 + 5y) (2(4 + 5y) + 3y * (4 + 5y)) = 0 ((4 * 2 + 5y * 2) + 3y * (4 + 5y)) = 0 ((8 + 10y) + 3y * (4 + 5y)) = 0 (8 + 10y + (4 * 3y + 5y * 3y)) = 0 (8 + 10y + (12y + 15y2)) = 0 Combine like terms: 10y + 12y = 22y (8 + 22y + 15y2) = 0 Solving 8 + 22y + 15y2 = 0 Solving for variable 'y'. Factor a trinomial. (4 + 5y)(2 + 3y) = 0Subproblem 1
Set the factor '(4 + 5y)' equal to zero and attempt to solve: Simplifying 4 + 5y = 0 Solving 4 + 5y = 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 + 5y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5y = 0 + -4 5y = 0 + -4 Combine like terms: 0 + -4 = -4 5y = -4 Divide each side by '5'. y = -0.8 Simplifying y = -0.8Subproblem 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 = {-0.8, -0.6666666667}
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