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Simplifying 4a4 + 56a3b + 192a2b2 = 0 Reorder the terms: 192a2b2 + 56a3b + 4a4 = 0 Solving 192a2b2 + 56a3b + 4a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4a2'. 4a2(48b2 + 14ab + a2) = 0 Factor a trinomial. 4a2((8b + a)(6b + a)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve: Simplifying a2 = 0 Solving a2 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a2 = 0 Take the square root of each side: a = {0}Subproblem 2
Set the factor '(8b + a)' equal to zero and attempt to solve: Simplifying 8b + a = 0 Reorder the terms: a + 8b = 0 Solving a + 8b = 0 Move all terms containing a to the left, all other terms to the right. Add '-8b' to each side of the equation. a + 8b + -8b = 0 + -8b Combine like terms: 8b + -8b = 0 a + 0 = 0 + -8b a = 0 + -8b Remove the zero: a = -8b Simplifying a = -8bSubproblem 3
Set the factor '(6b + a)' equal to zero and attempt to solve: Simplifying 6b + a = 0 Reorder the terms: a + 6b = 0 Solving a + 6b = 0 Move all terms containing a to the left, all other terms to the right. Add '-6b' to each side of the equation. a + 6b + -6b = 0 + -6b Combine like terms: 6b + -6b = 0 a + 0 = 0 + -6b a = 0 + -6b Remove the zero: a = -6b Simplifying a = -6bSolution
a = {0, -8b, -6b}
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