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