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Simplifying 5a3b + -45ab3 = 0 Reorder the terms: -45ab3 + 5a3b = 0 Solving -45ab3 + 5a3b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5ab'. 5ab(-9b2 + a2) = 0 Factor a difference between two squares. 5ab((3b + a)(-3b + a)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'ab' equal to zero and attempt to solve: Simplifying ab = 0 Solving ab = 0 Move all terms containing a to the left, all other terms to the right. Simplifying ab = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(3b + a)' equal to zero and attempt to solve: Simplifying 3b + a = 0 Reorder the terms: a + 3b = 0 Solving a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 a + 0 = 0 + -3b a = 0 + -3b Remove the zero: a = -3b Simplifying a = -3bSubproblem 3
Set the factor '(-3b + a)' equal to zero and attempt to solve: Simplifying -3b + a = 0 Reorder the terms: a + -3b = 0 Solving a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 a + 0 = 0 + 3b a = 0 + 3b Remove the zero: a = 3b Simplifying a = 3bSolution
a = {-3b, 3b}
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