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