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Simplifying 40y4 + 15y2 + -25y2 = 0 Reorder the terms: 15y2 + -25y2 + 40y4 = 0 Combine like terms: 15y2 + -25y2 = -10y2 -10y2 + 40y4 = 0 Solving -10y2 + 40y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '10y2'. 10y2(-1 + 4y2) = 0 Factor a difference between two squares. 10y2((1 + 2y)(-1 + 2y)) = 0 Ignore the factor 10.Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 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 = -0.5Subproblem 3
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 = {0, -0.5, 0.5}
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