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Simplifying z2 + 13az + 12a2 = 0 Reorder the terms: 13az + 12a2 + z2 = 0 Solving 13az + 12a2 + z2 = 0 Solving for variable 'a'. Factor a trinomial. (12a + z)(a + z) = 0Subproblem 1
Set the factor '(12a + z)' equal to zero and attempt to solve: Simplifying 12a + z = 0 Solving 12a + z = 0 Move all terms containing a to the left, all other terms to the right. Add '-1z' to each side of the equation. 12a + z + -1z = 0 + -1z Combine like terms: z + -1z = 0 12a + 0 = 0 + -1z 12a = 0 + -1z Remove the zero: 12a = -1z Divide each side by '12'. a = -0.08333333333z Simplifying a = -0.08333333333zSubproblem 2
Set the factor '(a + z)' equal to zero and attempt to solve: Simplifying a + z = 0 Solving a + z = 0 Move all terms containing a to the left, all other terms to the right. Add '-1z' to each side of the equation. a + z + -1z = 0 + -1z Combine like terms: z + -1z = 0 a + 0 = 0 + -1z a = 0 + -1z Remove the zero: a = -1z Simplifying a = -1zSolution
a = {-0.08333333333z, -1z}
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