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Simplifying (6y + 9)(5y + -2) = 0 Reorder the terms: (9 + 6y)(5y + -2) = 0 Reorder the terms: (9 + 6y)(-2 + 5y) = 0 Multiply (9 + 6y) * (-2 + 5y) (9(-2 + 5y) + 6y * (-2 + 5y)) = 0 ((-2 * 9 + 5y * 9) + 6y * (-2 + 5y)) = 0 ((-18 + 45y) + 6y * (-2 + 5y)) = 0 (-18 + 45y + (-2 * 6y + 5y * 6y)) = 0 (-18 + 45y + (-12y + 30y2)) = 0 Combine like terms: 45y + -12y = 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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