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Simplifying 0 = 2a2 + 5ab + 3b2 Reorder the terms: 0 = 5ab + 2a2 + 3b2 Solving 0 = 5ab + 2a2 + 3b2 Solving for variable 'a'. Remove the zero: -5ab + -2a2 + -3b2 = 5ab + 2a2 + 3b2 + -5ab + -2a2 + -3b2 Reorder the terms: -5ab + -2a2 + -3b2 = 5ab + -5ab + 2a2 + -2a2 + 3b2 + -3b2 Combine like terms: 5ab + -5ab = 0 -5ab + -2a2 + -3b2 = 0 + 2a2 + -2a2 + 3b2 + -3b2 -5ab + -2a2 + -3b2 = 2a2 + -2a2 + 3b2 + -3b2 Combine like terms: 2a2 + -2a2 = 0 -5ab + -2a2 + -3b2 = 0 + 3b2 + -3b2 -5ab + -2a2 + -3b2 = 3b2 + -3b2 Combine like terms: 3b2 + -3b2 = 0 -5ab + -2a2 + -3b2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5ab + 2a2 + 3b2) = 0 Factor a trinomial. -1((a + b)(2a + 3b)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(a + b)' equal to zero and attempt to solve: Simplifying a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1bSubproblem 2
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 = -1.5bSolution
a = {-1b, -1.5b}
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