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Simplifying y2 + 13ay + 12a2 = 0 Reorder the terms: 13ay + 12a2 + y2 = 0 Solving 13ay + 12a2 + y2 = 0 Solving for variable 'a'. Factor a trinomial. (12a + y)(a + y) = 0Subproblem 1
Set the factor '(12a + y)' equal to zero and attempt to solve: Simplifying 12a + y = 0 Solving 12a + y = 0 Move all terms containing a to the left, all other terms to the right. Add '-1y' to each side of the equation. 12a + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 12a + 0 = 0 + -1y 12a = 0 + -1y Remove the zero: 12a = -1y Divide each side by '12'. a = -0.08333333333y Simplifying a = -0.08333333333ySubproblem 2
Set the factor '(a + y)' equal to zero and attempt to solve: Simplifying a + y = 0 Solving a + y = 0 Move all terms containing a to the left, all other terms to the right. Add '-1y' to each side of the equation. a + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 a + 0 = 0 + -1y a = 0 + -1y Remove the zero: a = -1y Simplifying a = -1ySolution
a = {-0.08333333333y, -1y}
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