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Simplifying 24a4 + 10a3b + -4a2b2 = 0 Reorder the terms: -4a2b2 + 10a3b + 24a4 = 0 Solving -4a2b2 + 10a3b + 24a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a2'. 2a2(-2b2 + 5ab + 12a2) = 0 Factor a trinomial. 2a2((-2b + -3a)(b + -4a)) = 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 '(-2b + -3a)' equal to zero and attempt to solve: Simplifying -2b + -3a = 0 Reorder the terms: -3a + -2b = 0 Solving -3a + -2b = 0 Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. -3a + -2b + 2b = 0 + 2b Combine like terms: -2b + 2b = 0 -3a + 0 = 0 + 2b -3a = 0 + 2b Remove the zero: -3a = 2b Divide each side by '-3'. a = -0.6666666667b Simplifying a = -0.6666666667bSubproblem 3
Set the factor '(b + -4a)' equal to zero and attempt to solve: Simplifying b + -4a = 0 Reorder the terms: -4a + b = 0 Solving -4a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. -4a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 -4a + 0 = 0 + -1b -4a = 0 + -1b Remove the zero: -4a = -1b Divide each side by '-4'. a = 0.25b Simplifying a = 0.25bSolution
a = {0, -0.6666666667b, 0.25b}
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