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Simplifying (4a + -2b)(3a + 3b) = 0 Multiply (4a + -2b) * (3a + 3b) (4a * (3a + 3b) + -2b * (3a + 3b)) = 0 ((3a * 4a + 3b * 4a) + -2b * (3a + 3b)) = 0 Reorder the terms: ((12ab + 12a2) + -2b * (3a + 3b)) = 0 ((12ab + 12a2) + -2b * (3a + 3b)) = 0 (12ab + 12a2 + (3a * -2b + 3b * -2b)) = 0 (12ab + 12a2 + (-6ab + -6b2)) = 0 Reorder the terms: (12ab + -6ab + 12a2 + -6b2) = 0 Combine like terms: 12ab + -6ab = 6ab (6ab + 12a2 + -6b2) = 0 Solving 6ab + 12a2 + -6b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6'. 6(ab + 2a2 + -1b2) = 0 Factor a trinomial. 6((2a + -1b)(a + b)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2a + -1b)' equal to zero and attempt to solve: Simplifying 2a + -1b = 0 Solving 2a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 2a + -1b + b = 0 + b Combine like terms: -1b + b = 0 2a + 0 = 0 + b 2a = 0 + b Remove the zero: 2a = b Divide each side by '2'. a = 0.5b Simplifying a = 0.5bSubproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve: Simplifying a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1bSolution
a = {0.5b, -1b}
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