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Simplifying 2y2 + 5y + -9 = y2 + 2y + 1 Reorder the terms: -9 + 5y + 2y2 = y2 + 2y + 1 Reorder the terms: -9 + 5y + 2y2 = 1 + 2y + y2 Solving -9 + 5y + 2y2 = 1 + 2y + y2 Solving for variable 'y'. Reorder the terms: -9 + -1 + 5y + -2y + 2y2 + -1y2 = 1 + 2y + y2 + -1 + -2y + -1y2 Combine like terms: -9 + -1 = -10 -10 + 5y + -2y + 2y2 + -1y2 = 1 + 2y + y2 + -1 + -2y + -1y2 Combine like terms: 5y + -2y = 3y -10 + 3y + 2y2 + -1y2 = 1 + 2y + y2 + -1 + -2y + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 -10 + 3y + 1y2 = 1 + 2y + y2 + -1 + -2y + -1y2 Reorder the terms: -10 + 3y + 1y2 = 1 + -1 + 2y + -2y + y2 + -1y2 Combine like terms: 1 + -1 = 0 -10 + 3y + 1y2 = 0 + 2y + -2y + y2 + -1y2 -10 + 3y + 1y2 = 2y + -2y + y2 + -1y2 Combine like terms: 2y + -2y = 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 + -1y) = 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 + -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 = 2Solution
y = {-5, 2}
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