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