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Simplifying 80y4 + -45y2 = 0 Reorder the terms: -45y2 + 80y4 = 0 Solving -45y2 + 80y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y2'. 5y2(-9 + 16y2) = 0 Factor a difference between two squares. 5y2((3 + 4y)(-3 + 4y)) = 0 Ignore the factor 5.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 '(3 + 4y)' equal to zero and attempt to solve: Simplifying 3 + 4y = 0 Solving 3 + 4y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4y = 0 + -3 4y = 0 + -3 Combine like terms: 0 + -3 = -3 4y = -3 Divide each side by '4'. y = -0.75 Simplifying y = -0.75Subproblem 3
Set the factor '(-3 + 4y)' equal to zero and attempt to solve: Simplifying -3 + 4y = 0 Solving -3 + 4y = 0 Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 4y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4y = 0 + 3 4y = 0 + 3 Combine like terms: 0 + 3 = 3 4y = 3 Divide each side by '4'. y = 0.75 Simplifying y = 0.75Solution
y = {0, -0.75, 0.75}
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