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Simplifying 81a3 + -4ay2 = 0 Reorder the terms: -4ay2 + 81a3 = 0 Solving -4ay2 + 81a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-4y2 + 81a2) = 0 Factor a difference between two squares. a((2y + 9a)(-2y + 9a)) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(2y + 9a)' equal to zero and attempt to solve: Simplifying 2y + 9a = 0 Reorder the terms: 9a + 2y = 0 Solving 9a + 2y = 0 Move all terms containing a to the left, all other terms to the right. Add '-2y' to each side of the equation. 9a + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 9a + 0 = 0 + -2y 9a = 0 + -2y Remove the zero: 9a = -2y Divide each side by '9'. a = -0.2222222222y Simplifying a = -0.2222222222ySubproblem 3
Set the factor '(-2y + 9a)' equal to zero and attempt to solve: Simplifying -2y + 9a = 0 Reorder the terms: 9a + -2y = 0 Solving 9a + -2y = 0 Move all terms containing a to the left, all other terms to the right. Add '2y' to each side of the equation. 9a + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 9a + 0 = 0 + 2y 9a = 0 + 2y Remove the zero: 9a = 2y Divide each side by '9'. a = 0.2222222222y Simplifying a = 0.2222222222ySolution
a = {0, -0.2222222222y, 0.2222222222y}
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