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Simplifying 32a4z + -144a2z + 162z = 0 Reorder the terms: -144a2z + 32a4z + 162z = 0 Solving -144a2z + 32a4z + 162z = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2z'. 2z(-72a2 + 16a4 + 81) = 0 Factor a trinomial. 2z((4a2 + -9)(4a2 + -9)) = 0 Factor a difference between two squares. 2z(((2a + 3)(2a + -3))(4a2 + -9)) = 0 Factor a difference between two squares. 2z(((2a + 3)(2a + -3))(2a + 3)(2a + -3)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing a to the left, all other terms to the right. Add '-1z' to each side of the equation. z + -1z = 0 + -1z Remove the zero: 0 = -1z Simplifying 0 = -1z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2a + 3)' equal to zero and attempt to solve: Simplifying 2a + 3 = 0 Reorder the terms: 3 + 2a = 0 Solving 3 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2a = 0 + -3 2a = 0 + -3 Combine like terms: 0 + -3 = -3 2a = -3 Divide each side by '2'. a = -1.5 Simplifying a = -1.5Subproblem 3
Set the factor '(2a + -3)' equal to zero and attempt to solve: Simplifying 2a + -3 = 0 Reorder the terms: -3 + 2a = 0 Solving -3 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2a = 0 + 3 2a = 0 + 3 Combine like terms: 0 + 3 = 3 2a = 3 Divide each side by '2'. a = 1.5 Simplifying a = 1.5Subproblem 4
Set the factor '(2a + 3)' equal to zero and attempt to solve: Simplifying 2a + 3 = 0 Reorder the terms: 3 + 2a = 0 Solving 3 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2a = 0 + -3 2a = 0 + -3 Combine like terms: 0 + -3 = -3 2a = -3 Divide each side by '2'. a = -1.5 Simplifying a = -1.5Subproblem 5
Set the factor '(2a + -3)' equal to zero and attempt to solve: Simplifying 2a + -3 = 0 Reorder the terms: -3 + 2a = 0 Solving -3 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2a = 0 + 3 2a = 0 + 3 Combine like terms: 0 + 3 = 3 2a = 3 Divide each side by '2'. a = 1.5 Simplifying a = 1.5Solution
a = {-1.5, 1.5, -1.5, 1.5}
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