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Simplifying (4y + -2)(4y + 2) + (4y + -2)(y + 8) = 0 Reorder the terms: (-2 + 4y)(4y + 2) + (4y + -2)(y + 8) = 0 Reorder the terms: (-2 + 4y)(2 + 4y) + (4y + -2)(y + 8) = 0 Multiply (-2 + 4y) * (2 + 4y) (-2(2 + 4y) + 4y * (2 + 4y)) + (4y + -2)(y + 8) = 0 ((2 * -2 + 4y * -2) + 4y * (2 + 4y)) + (4y + -2)(y + 8) = 0 ((-4 + -8y) + 4y * (2 + 4y)) + (4y + -2)(y + 8) = 0 (-4 + -8y + (2 * 4y + 4y * 4y)) + (4y + -2)(y + 8) = 0 (-4 + -8y + (8y + 16y2)) + (4y + -2)(y + 8) = 0 Combine like terms: -8y + 8y = 0 (-4 + 0 + 16y2) + (4y + -2)(y + 8) = 0 (-4 + 16y2) + (4y + -2)(y + 8) = 0 Reorder the terms: -4 + 16y2 + (-2 + 4y)(y + 8) = 0 Reorder the terms: -4 + 16y2 + (-2 + 4y)(8 + y) = 0 Multiply (-2 + 4y) * (8 + y) -4 + 16y2 + (-2(8 + y) + 4y * (8 + y)) = 0 -4 + 16y2 + ((8 * -2 + y * -2) + 4y * (8 + y)) = 0 -4 + 16y2 + ((-16 + -2y) + 4y * (8 + y)) = 0 -4 + 16y2 + (-16 + -2y + (8 * 4y + y * 4y)) = 0 -4 + 16y2 + (-16 + -2y + (32y + 4y2)) = 0 Combine like terms: -2y + 32y = 30y -4 + 16y2 + (-16 + 30y + 4y2) = 0 Reorder the terms: -4 + -16 + 30y + 16y2 + 4y2 = 0 Combine like terms: -4 + -16 = -20 -20 + 30y + 16y2 + 4y2 = 0 Combine like terms: 16y2 + 4y2 = 20y2 -20 + 30y + 20y2 = 0 Solving -20 + 30y + 20y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '10'. 10(-2 + 3y + 2y2) = 0 Factor a trinomial. 10((-2 + -1y)(1 + -2y)) = 0 Ignore the factor 10.Subproblem 1
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 = -2Subproblem 2
Set the factor '(1 + -2y)' equal to zero and attempt to solve: Simplifying 1 + -2y = 0 Solving 1 + -2y = 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 + -2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2y = 0 + -1 -2y = 0 + -1 Combine like terms: 0 + -1 = -1 -2y = -1 Divide each side by '-2'. y = 0.5 Simplifying y = 0.5Solution
y = {-2, 0.5}
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