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Simplifying (7y2 + -5y + -1) + (3y2 + -6y + 4) = 0 Reorder the terms: (-1 + -5y + 7y2) + (3y2 + -6y + 4) = 0 Remove parenthesis around (-1 + -5y + 7y2) -1 + -5y + 7y2 + (3y2 + -6y + 4) = 0 Reorder the terms: -1 + -5y + 7y2 + (4 + -6y + 3y2) = 0 Remove parenthesis around (4 + -6y + 3y2) -1 + -5y + 7y2 + 4 + -6y + 3y2 = 0 Reorder the terms: -1 + 4 + -5y + -6y + 7y2 + 3y2 = 0 Combine like terms: -1 + 4 = 3 3 + -5y + -6y + 7y2 + 3y2 = 0 Combine like terms: -5y + -6y = -11y 3 + -11y + 7y2 + 3y2 = 0 Combine like terms: 7y2 + 3y2 = 10y2 3 + -11y + 10y2 = 0 Solving 3 + -11y + 10y2 = 0 Solving for variable 'y'. Factor a trinomial. (1 + -2y)(3 + -5y) = 0Subproblem 1
Set the factor '(1 + -2y)' equal to zero and attempt to solve: Simplifying 1 + -2y = 0 Solving 1 + -2y = 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 + -2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2y = 0 + -1 -2y = 0 + -1 Combine like terms: 0 + -1 = -1 -2y = -1 Divide each side by '-2'. y = 0.5 Simplifying y = 0.5Subproblem 2
Set the factor '(3 + -5y)' equal to zero and attempt to solve: Simplifying 3 + -5y = 0 Solving 3 + -5y = 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 + -5y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5y = 0 + -3 -5y = 0 + -3 Combine like terms: 0 + -3 = -3 -5y = -3 Divide each side by '-5'. y = 0.6 Simplifying y = 0.6Solution
y = {0.5, 0.6}
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