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Simplifying (y2 + -3)(y2 + 5) = 9 Reorder the terms: (-3 + y2)(y2 + 5) = 9 Reorder the terms: (-3 + y2)(5 + y2) = 9 Multiply (-3 + y2) * (5 + y2) (-3(5 + y2) + y2(5 + y2)) = 9 ((5 * -3 + y2 * -3) + y2(5 + y2)) = 9 ((-15 + -3y2) + y2(5 + y2)) = 9 (-15 + -3y2 + (5 * y2 + y2 * y2)) = 9 (-15 + -3y2 + (5y2 + y4)) = 9 Combine like terms: -3y2 + 5y2 = 2y2 (-15 + 2y2 + y4) = 9 Solving -15 + 2y2 + y4 = 9 Solving for variable 'y'. Reorder the terms: -15 + -9 + 2y2 + y4 = 9 + -9 Combine like terms: -15 + -9 = -24 -24 + 2y2 + y4 = 9 + -9 Combine like terms: 9 + -9 = 0 -24 + 2y2 + y4 = 0 Factor a trinomial. (-6 + -1y2)(4 + -1y2) = 0 Factor a difference between two squares. (-6 + -1y2)((2 + y)(2 + -1y)) = 0Subproblem 1
Set the factor '(-6 + -1y2)' equal to zero and attempt to solve: Simplifying -6 + -1y2 = 0 Solving -6 + -1y2 = 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 + -1y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1y2 = 0 + 6 -1y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1y2 = 6 Divide each side by '-1'. y2 = -6 Simplifying y2 = -6 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 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 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2Subproblem 3
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 = {-2, 2}
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