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Simplifying (5y + -2)(6y + 9) = 0 Reorder the terms: (-2 + 5y)(6y + 9) = 0 Reorder the terms: (-2 + 5y)(9 + 6y) = 0 Multiply (-2 + 5y) * (9 + 6y) (-2(9 + 6y) + 5y * (9 + 6y)) = 0 ((9 * -2 + 6y * -2) + 5y * (9 + 6y)) = 0 ((-18 + -12y) + 5y * (9 + 6y)) = 0 (-18 + -12y + (9 * 5y + 6y * 5y)) = 0 (-18 + -12y + (45y + 30y2)) = 0 Combine like terms: -12y + 45y = 33y (-18 + 33y + 30y2) = 0 Solving -18 + 33y + 30y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 11y + 10y2) = 0 Factor a trinomial. 3((-3 + -2y)(2 + -5y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -2y)' equal to zero and attempt to solve: Simplifying -3 + -2y = 0 Solving -3 + -2y = 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 + -2y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2y = 0 + 3 -2y = 0 + 3 Combine like terms: 0 + 3 = 3 -2y = 3 Divide each side by '-2'. y = -1.5 Simplifying y = -1.5Subproblem 2
Set the factor '(2 + -5y)' equal to zero and attempt to solve: Simplifying 2 + -5y = 0 Solving 2 + -5y = 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 + -5y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5y = 0 + -2 -5y = 0 + -2 Combine like terms: 0 + -2 = -2 -5y = -2 Divide each side by '-5'. y = 0.4 Simplifying y = 0.4Solution
y = {-1.5, 0.4}
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