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Simplifying (2y + -3)(2y + -3) + -2(y + 1)(y + 1) + 7 = 0 Reorder the terms: (-3 + 2y)(2y + -3) + -2(y + 1)(y + 1) + 7 = 0 Reorder the terms: (-3 + 2y)(-3 + 2y) + -2(y + 1)(y + 1) + 7 = 0 Multiply (-3 + 2y) * (-3 + 2y) (-3(-3 + 2y) + 2y * (-3 + 2y)) + -2(y + 1)(y + 1) + 7 = 0 ((-3 * -3 + 2y * -3) + 2y * (-3 + 2y)) + -2(y + 1)(y + 1) + 7 = 0 ((9 + -6y) + 2y * (-3 + 2y)) + -2(y + 1)(y + 1) + 7 = 0 (9 + -6y + (-3 * 2y + 2y * 2y)) + -2(y + 1)(y + 1) + 7 = 0 (9 + -6y + (-6y + 4y2)) + -2(y + 1)(y + 1) + 7 = 0 Combine like terms: -6y + -6y = -12y (9 + -12y + 4y2) + -2(y + 1)(y + 1) + 7 = 0 Reorder the terms: 9 + -12y + 4y2 + -2(1 + y)(y + 1) + 7 = 0 Reorder the terms: 9 + -12y + 4y2 + -2(1 + y)(1 + y) + 7 = 0 Multiply (1 + y) * (1 + y) 9 + -12y + 4y2 + -2(1(1 + y) + y(1 + y)) + 7 = 0 9 + -12y + 4y2 + -2((1 * 1 + y * 1) + y(1 + y)) + 7 = 0 9 + -12y + 4y2 + -2((1 + 1y) + y(1 + y)) + 7 = 0 9 + -12y + 4y2 + -2(1 + 1y + (1 * y + y * y)) + 7 = 0 9 + -12y + 4y2 + -2(1 + 1y + (1y + y2)) + 7 = 0 Combine like terms: 1y + 1y = 2y 9 + -12y + 4y2 + -2(1 + 2y + y2) + 7 = 0 9 + -12y + 4y2 + (1 * -2 + 2y * -2 + y2 * -2) + 7 = 0 9 + -12y + 4y2 + (-2 + -4y + -2y2) + 7 = 0 Reorder the terms: 9 + -2 + 7 + -12y + -4y + 4y2 + -2y2 = 0 Combine like terms: 9 + -2 = 7 7 + 7 + -12y + -4y + 4y2 + -2y2 = 0 Combine like terms: 7 + 7 = 14 14 + -12y + -4y + 4y2 + -2y2 = 0 Combine like terms: -12y + -4y = -16y 14 + -16y + 4y2 + -2y2 = 0 Combine like terms: 4y2 + -2y2 = 2y2 14 + -16y + 2y2 = 0 Solving 14 + -16y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -8y + y2) = 0 Factor a trinomial. 2((1 + -1y)(7 + -1y)) = 0 Ignore the factor 2.Subproblem 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 '(7 + -1y)' equal to zero and attempt to solve: Simplifying 7 + -1y = 0 Solving 7 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1y = 0 + -7 -1y = 0 + -7 Combine like terms: 0 + -7 = -7 -1y = -7 Divide each side by '-1'. y = 7 Simplifying y = 7Solution
y = {1, 7}
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