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