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Simplifying (5y + 2)(8y + -3) = 0 Reorder the terms: (2 + 5y)(8y + -3) = 0 Reorder the terms: (2 + 5y)(-3 + 8y) = 0 Multiply (2 + 5y) * (-3 + 8y) (2(-3 + 8y) + 5y * (-3 + 8y)) = 0 ((-3 * 2 + 8y * 2) + 5y * (-3 + 8y)) = 0 ((-6 + 16y) + 5y * (-3 + 8y)) = 0 (-6 + 16y + (-3 * 5y + 8y * 5y)) = 0 (-6 + 16y + (-15y + 40y2)) = 0 Combine like terms: 16y + -15y = 1y (-6 + 1y + 40y2) = 0 Solving -6 + 1y + 40y2 = 0 Solving for variable 'y'. Factor a trinomial. (-2 + -5y)(3 + -8y) = 0Subproblem 1
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 = -0.4Subproblem 2
Set the factor '(3 + -8y)' equal to zero and attempt to solve: Simplifying 3 + -8y = 0 Solving 3 + -8y = 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 + -8y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8y = 0 + -3 -8y = 0 + -3 Combine like terms: 0 + -3 = -3 -8y = -3 Divide each side by '-8'. y = 0.375 Simplifying y = 0.375Solution
y = {-0.4, 0.375}
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