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Simplifying (5a + -3b)(a + b) = 0 Multiply (5a + -3b) * (a + b) (5a * (a + b) + -3b * (a + b)) = 0 ((a * 5a + b * 5a) + -3b * (a + b)) = 0 Reorder the terms: ((5ab + 5a2) + -3b * (a + b)) = 0 ((5ab + 5a2) + -3b * (a + b)) = 0 (5ab + 5a2 + (a * -3b + b * -3b)) = 0 (5ab + 5a2 + (-3ab + -3b2)) = 0 Reorder the terms: (5ab + -3ab + 5a2 + -3b2) = 0 Combine like terms: 5ab + -3ab = 2ab (2ab + 5a2 + -3b2) = 0 Solving 2ab + 5a2 + -3b2 = 0 Solving for variable 'a'. Factor a trinomial. (5a + -3b)(a + b) = 0Subproblem 1
Set the factor '(5a + -3b)' equal to zero and attempt to solve: Simplifying 5a + -3b = 0 Solving 5a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 5a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 5a + 0 = 0 + 3b 5a = 0 + 3b Remove the zero: 5a = 3b Divide each side by '5'. a = 0.6b Simplifying a = 0.6bSubproblem 2
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 = -1bSolution
a = {0.6b, -1b}
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