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Simplifying 3y2 + 2y + -3y + 6 = 5y2 + 10y Reorder the terms: 6 + 2y + -3y + 3y2 = 5y2 + 10y Combine like terms: 2y + -3y = -1y 6 + -1y + 3y2 = 5y2 + 10y Reorder the terms: 6 + -1y + 3y2 = 10y + 5y2 Solving 6 + -1y + 3y2 = 10y + 5y2 Solving for variable 'y'. Reorder the terms: 6 + -1y + -10y + 3y2 + -5y2 = 10y + 5y2 + -10y + -5y2 Combine like terms: -1y + -10y = -11y 6 + -11y + 3y2 + -5y2 = 10y + 5y2 + -10y + -5y2 Combine like terms: 3y2 + -5y2 = -2y2 6 + -11y + -2y2 = 10y + 5y2 + -10y + -5y2 Reorder the terms: 6 + -11y + -2y2 = 10y + -10y + 5y2 + -5y2 Combine like terms: 10y + -10y = 0 6 + -11y + -2y2 = 0 + 5y2 + -5y2 6 + -11y + -2y2 = 5y2 + -5y2 Combine like terms: 5y2 + -5y2 = 0 6 + -11y + -2y2 = 0 Factor a trinomial. (1 + -2y)(6 + y) = 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 '(6 + y)' equal to zero and attempt to solve: Simplifying 6 + y = 0 Solving 6 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + y = 0 + -6 y = 0 + -6 Combine like terms: 0 + -6 = -6 y = -6 Simplifying y = -6Solution
y = {0.5, -6}
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