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Simplifying 0 = 2y(5y3 + 4)(5y3 + -4) Reorder the terms: 0 = 2y(4 + 5y3)(5y3 + -4) Reorder the terms: 0 = 2y(4 + 5y3)(-4 + 5y3) Multiply (4 + 5y3) * (-4 + 5y3) 0 = 2y(4(-4 + 5y3) + 5y3 * (-4 + 5y3)) 0 = 2y((-4 * 4 + 5y3 * 4) + 5y3 * (-4 + 5y3)) 0 = 2y((-16 + 20y3) + 5y3 * (-4 + 5y3)) 0 = 2y(-16 + 20y3 + (-4 * 5y3 + 5y3 * 5y3)) 0 = 2y(-16 + 20y3 + (-20y3 + 25y6)) Combine like terms: 20y3 + -20y3 = 0 0 = 2y(-16 + 0 + 25y6) 0 = 2y(-16 + 25y6) 0 = (-16 * 2y + 25y6 * 2y) 0 = (-32y + 50y7) Solving 0 = -32y + 50y7 Solving for variable 'y'. Remove the zero: 32y + -50y7 = -32y + 50y7 + 32y + -50y7 Reorder the terms: 32y + -50y7 = -32y + 32y + 50y7 + -50y7 Combine like terms: -32y + 32y = 0 32y + -50y7 = 0 + 50y7 + -50y7 32y + -50y7 = 50y7 + -50y7 Combine like terms: 50y7 + -50y7 = 0 32y + -50y7 = 0 Factor out the Greatest Common Factor (GCF), '2y'. 2y(16 + -25y6) = 0 Factor a difference between two squares. 2y((4 + 5y3)(4 + -5y3)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(4 + 5y3)' equal to zero and attempt to solve: Simplifying 4 + 5y3 = 0 Solving 4 + 5y3 = 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 + 5y3 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5y3 = 0 + -4 5y3 = 0 + -4 Combine like terms: 0 + -4 = -4 5y3 = -4 Divide each side by '5'. y3 = -0.8 Simplifying y3 = -0.8 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(4 + -5y3)' equal to zero and attempt to solve: Simplifying 4 + -5y3 = 0 Solving 4 + -5y3 = 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 + -5y3 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5y3 = 0 + -4 -5y3 = 0 + -4 Combine like terms: 0 + -4 = -4 -5y3 = -4 Divide each side by '-5'. y3 = 0.8 Simplifying y3 = 0.8 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
y = {0}
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