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Simplifying 6y2 = 13y + -5 Reorder the terms: 6y2 = -5 + 13y Solving 6y2 = -5 + 13y Solving for variable 'y'. Reorder the terms: 5 + -13y + 6y2 = -5 + 13y + 5 + -13y Reorder the terms: 5 + -13y + 6y2 = -5 + 5 + 13y + -13y Combine like terms: -5 + 5 = 0 5 + -13y + 6y2 = 0 + 13y + -13y 5 + -13y + 6y2 = 13y + -13y Combine like terms: 13y + -13y = 0 5 + -13y + 6y2 = 0 Factor a trinomial. (1 + -2y)(5 + -3y) = 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 '(5 + -3y)' equal to zero and attempt to solve: Simplifying 5 + -3y = 0 Solving 5 + -3y = 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 + -3y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3y = 0 + -5 -3y = 0 + -5 Combine like terms: 0 + -5 = -5 -3y = -5 Divide each side by '-3'. y = 1.666666667 Simplifying y = 1.666666667Solution
y = {0.5, 1.666666667}
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