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Simplifying (2y + 5)(3y + -2) = 0 Reorder the terms: (5 + 2y)(3y + -2) = 0 Reorder the terms: (5 + 2y)(-2 + 3y) = 0 Multiply (5 + 2y) * (-2 + 3y) (5(-2 + 3y) + 2y * (-2 + 3y)) = 0 ((-2 * 5 + 3y * 5) + 2y * (-2 + 3y)) = 0 ((-10 + 15y) + 2y * (-2 + 3y)) = 0 (-10 + 15y + (-2 * 2y + 3y * 2y)) = 0 (-10 + 15y + (-4y + 6y2)) = 0 Combine like terms: 15y + -4y = 11y (-10 + 11y + 6y2) = 0 Solving -10 + 11y + 6y2 = 0 Solving for variable 'y'. Factor a trinomial. (-5 + -2y)(2 + -3y) = 0Subproblem 1
Set the factor '(-5 + -2y)' equal to zero and attempt to solve: Simplifying -5 + -2y = 0 Solving -5 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2y = 0 + 5 -2y = 0 + 5 Combine like terms: 0 + 5 = 5 -2y = 5 Divide each side by '-2'. y = -2.5 Simplifying y = -2.5Subproblem 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 = {-2.5, 0.6666666667}
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