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Simplifying 40a4 + 50a3b + -15a2b2 = 0 Reorder the terms: -15a2b2 + 50a3b + 40a4 = 0 Solving -15a2b2 + 50a3b + 40a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a2'. 5a2(-3b2 + 10ab + 8a2) = 0 Factor a trinomial. 5a2((-3b + -2a)(b + -4a)) = 0 Ignore the factor 5.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 '(-3b + -2a)' equal to zero and attempt to solve: Simplifying -3b + -2a = 0 Reorder the terms: -2a + -3b = 0 Solving -2a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. -2a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 -2a + 0 = 0 + 3b -2a = 0 + 3b Remove the zero: -2a = 3b Divide each side by '-2'. a = -1.5b Simplifying a = -1.5bSubproblem 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, -1.5b, 0.25b}
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