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Simplifying 3a(4a + -2b + c) = 0 (4a * 3a + -2b * 3a + c * 3a) = 0 Reorder the terms: (-6ab + 3ac + 12a2) = 0 (-6ab + 3ac + 12a2) = 0 Solving -6ab + 3ac + 12a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a'. 3a(-2b + c + 4a) = 0 Ignore the factor 3.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 '(-2b + c + 4a)' equal to zero and attempt to solve: Simplifying -2b + c + 4a = 0 Reorder the terms: 4a + -2b + c = 0 Solving 4a + -2b + c = 0 Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. 4a + -2b + 2b + c = 0 + 2b Combine like terms: -2b + 2b = 0 4a + 0 + c = 0 + 2b 4a + c = 0 + 2b Remove the zero: 4a + c = 2b Add '-1c' to each side of the equation. 4a + c + -1c = 2b + -1c Combine like terms: c + -1c = 0 4a + 0 = 2b + -1c 4a = 2b + -1c Divide each side by '4'. a = 0.5b + -0.25c Simplifying a = 0.5b + -0.25cSolution
a = {0, 0.5b + -0.25c}
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