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Simplifying 6ab2 + -24a3 = 0 Solving 6ab2 + -24a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6a'. 6a(b2 + -4a2) = 0 Factor a difference between two squares. 6a((b + 2a)(b + -2a)) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(b + 2a)' equal to zero and attempt to solve: Simplifying b + 2a = 0 Reorder the terms: 2a + b = 0 Solving 2a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 2a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 2a + 0 = 0 + -1b 2a = 0 + -1b Remove the zero: 2a = -1b Divide each side by '2'. a = -0.5b Simplifying a = -0.5bSubproblem 3
Set the factor '(b + -2a)' equal to zero and attempt to solve: Simplifying b + -2a = 0 Reorder the terms: -2a + b = 0 Solving -2a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. -2a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 -2a + 0 = 0 + -1b -2a = 0 + -1b Remove the zero: -2a = -1b Divide each side by '-2'. a = 0.5b Simplifying a = 0.5bSolution
a = {0, -0.5b, 0.5b}
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