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Simplifying (y2 + -3)(y2 + -3) + 4(y2 + -3) + 4 = 0 Reorder the terms: (-3 + y2)(y2 + -3) + 4(y2 + -3) + 4 = 0 Reorder the terms: (-3 + y2)(-3 + y2) + 4(y2 + -3) + 4 = 0 Multiply (-3 + y2) * (-3 + y2) (-3(-3 + y2) + y2(-3 + y2)) + 4(y2 + -3) + 4 = 0 ((-3 * -3 + y2 * -3) + y2(-3 + y2)) + 4(y2 + -3) + 4 = 0 ((9 + -3y2) + y2(-3 + y2)) + 4(y2 + -3) + 4 = 0 (9 + -3y2 + (-3 * y2 + y2 * y2)) + 4(y2 + -3) + 4 = 0 (9 + -3y2 + (-3y2 + y4)) + 4(y2 + -3) + 4 = 0 Combine like terms: -3y2 + -3y2 = -6y2 (9 + -6y2 + y4) + 4(y2 + -3) + 4 = 0 Reorder the terms: 9 + -6y2 + y4 + 4(-3 + y2) + 4 = 0 9 + -6y2 + y4 + (-3 * 4 + y2 * 4) + 4 = 0 9 + -6y2 + y4 + (-12 + 4y2) + 4 = 0 Reorder the terms: 9 + -12 + 4 + -6y2 + 4y2 + y4 = 0 Combine like terms: 9 + -12 = -3 -3 + 4 + -6y2 + 4y2 + y4 = 0 Combine like terms: -3 + 4 = 1 1 + -6y2 + 4y2 + y4 = 0 Combine like terms: -6y2 + 4y2 = -2y2 1 + -2y2 + y4 = 0 Solving 1 + -2y2 + y4 = 0 Solving for variable 'y'. Factor a trinomial. (1 + -1y2)(1 + -1y2) = 0 Factor a difference between two squares. ((1 + y)(1 + -1y))(1 + -1y2) = 0 Factor a difference between two squares. ((1 + y)(1 + -1y))(1 + y)(1 + -1y) = 0Subproblem 1
Set the factor '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 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 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Simplifying y = -1Subproblem 2
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 3
Set the factor '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 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 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Simplifying y = -1Subproblem 4
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 = 1Solution
y = {-1, 1, -1, 1}
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