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Simplifying -8a2 + -30ab + -27b2 = 0 Reorder the terms: -30ab + -8a2 + -27b2 = 0 Solving -30ab + -8a2 + -27b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1'. -1(30ab + 8a2 + 27b2) = 0 Factor a trinomial. -1((2a + 3b)(4a + 9b)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2a + 3b)' equal to zero and attempt to solve: Simplifying 2a + 3b = 0 Solving 2a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 2a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 2a + 0 = 0 + -3b 2a = 0 + -3b Remove the zero: 2a = -3b Divide each side by '2'. a = -1.5b Simplifying a = -1.5bSubproblem 2
Set the factor '(4a + 9b)' equal to zero and attempt to solve: Simplifying 4a + 9b = 0 Solving 4a + 9b = 0 Move all terms containing a to the left, all other terms to the right. Add '-9b' to each side of the equation. 4a + 9b + -9b = 0 + -9b Combine like terms: 9b + -9b = 0 4a + 0 = 0 + -9b 4a = 0 + -9b Remove the zero: 4a = -9b Divide each side by '4'. a = -2.25b Simplifying a = -2.25bSolution
a = {-1.5b, -2.25b}
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