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Simplifying 2y2 + -5y + -3 = y2 + -6y + 9 Reorder the terms: -3 + -5y + 2y2 = y2 + -6y + 9 Reorder the terms: -3 + -5y + 2y2 = 9 + -6y + y2 Solving -3 + -5y + 2y2 = 9 + -6y + y2 Solving for variable 'y'. Reorder the terms: -3 + -9 + -5y + 6y + 2y2 + -1y2 = 9 + -6y + y2 + -9 + 6y + -1y2 Combine like terms: -3 + -9 = -12 -12 + -5y + 6y + 2y2 + -1y2 = 9 + -6y + y2 + -9 + 6y + -1y2 Combine like terms: -5y + 6y = 1y -12 + 1y + 2y2 + -1y2 = 9 + -6y + y2 + -9 + 6y + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 -12 + 1y + 1y2 = 9 + -6y + y2 + -9 + 6y + -1y2 Reorder the terms: -12 + 1y + 1y2 = 9 + -9 + -6y + 6y + y2 + -1y2 Combine like terms: 9 + -9 = 0 -12 + 1y + 1y2 = 0 + -6y + 6y + y2 + -1y2 -12 + 1y + 1y2 = -6y + 6y + y2 + -1y2 Combine like terms: -6y + 6y = 0 -12 + 1y + 1y2 = 0 + y2 + -1y2 -12 + 1y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -12 + 1y + 1y2 = 0 Factor a trinomial. (-4 + -1y)(3 + -1y) = 0Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve: Simplifying -4 + -1y = 0 Solving -4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1y = 0 + 4 -1y = 0 + 4 Combine like terms: 0 + 4 = 4 -1y = 4 Divide each side by '-1'. y = -4 Simplifying y = -4Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve: Simplifying 3 + -1y = 0 Solving 3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y = 0 + -3 -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1y = -3 Divide each side by '-1'. y = 3 Simplifying y = 3Solution
y = {-4, 3}
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