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Simplifying 5y(2y + -3) + (2y + -3) = 0 Reorder the terms: 5y(-3 + 2y) + (2y + -3) = 0 (-3 * 5y + 2y * 5y) + (2y + -3) = 0 (-15y + 10y2) + (2y + -3) = 0 Reorder the terms: -15y + 10y2 + (-3 + 2y) = 0 Remove parenthesis around (-3 + 2y) -15y + 10y2 + -3 + 2y = 0 Reorder the terms: -3 + -15y + 2y + 10y2 = 0 Combine like terms: -15y + 2y = -13y -3 + -13y + 10y2 = 0 Solving -3 + -13y + 10y2 = 0 Solving for variable 'y'. Factor a trinomial. (-1 + -5y)(3 + -2y) = 0Subproblem 1
Set the factor '(-1 + -5y)' equal to zero and attempt to solve: Simplifying -1 + -5y = 0 Solving -1 + -5y = 0 Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -5y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5y = 0 + 1 -5y = 0 + 1 Combine like terms: 0 + 1 = 1 -5y = 1 Divide each side by '-5'. y = -0.2 Simplifying y = -0.2Subproblem 2
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 = 1.5Solution
y = {-0.2, 1.5}
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