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Simplifying 24a2 + 10a3b + -4a2b2 = 0 Reorder the terms: 24a2 + -4a2b2 + 10a3b = 0 Solving 24a2 + -4a2b2 + 10a3b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a2'. 2a2(12 + -2b2 + 5ab) = 0 Ignore the factor 2.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 '(12 + -2b2 + 5ab)' equal to zero and attempt to solve: Simplifying 12 + -2b2 + 5ab = 0 Reorder the terms: 12 + 5ab + -2b2 = 0 Solving 12 + 5ab + -2b2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 5ab + -12 + -2b2 = 0 + -12 Reorder the terms: 12 + -12 + 5ab + -2b2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 5ab + -2b2 = 0 + -12 5ab + -2b2 = 0 + -12 Combine like terms: 0 + -12 = -12 5ab + -2b2 = -12 Add '2b2' to each side of the equation. 5ab + -2b2 + 2b2 = -12 + 2b2 Combine like terms: -2b2 + 2b2 = 0 5ab + 0 = -12 + 2b2 5ab = -12 + 2b2 Divide each side by '5b'. a = -2.4b-1 + 0.4b Simplifying a = -2.4b-1 + 0.4bSolution
a = {0, -2.4b-1 + 0.4b}
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