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Simplifying 6a(2a + -1b) + 2a(-4a + 5b) = 0 (2a * 6a + -1b * 6a) + 2a(-4a + 5b) = 0 Reorder the terms: (-6ab + 12a2) + 2a(-4a + 5b) = 0 (-6ab + 12a2) + 2a(-4a + 5b) = 0 -6ab + 12a2 + (-4a * 2a + 5b * 2a) = 0 Reorder the terms: -6ab + 12a2 + (10ab + -8a2) = 0 -6ab + 12a2 + (10ab + -8a2) = 0 Reorder the terms: -6ab + 10ab + 12a2 + -8a2 = 0 Combine like terms: -6ab + 10ab = 4ab 4ab + 12a2 + -8a2 = 0 Combine like terms: 12a2 + -8a2 = 4a2 4ab + 4a2 = 0 Solving 4ab + 4a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4a'. 4a(b + a) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(b + a)' equal to zero and attempt to solve: Simplifying b + a = 0 Reorder the terms: 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, -1b}
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