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Simplifying 5a(7a + 2b + -3c) = 0 (7a * 5a + 2b * 5a + -3c * 5a) = 0 Reorder the terms: (10ab + -15ac + 35a2) = 0 (10ab + -15ac + 35a2) = 0 Solving 10ab + -15ac + 35a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a'. 5a(2b + -3c + 7a) = 0 Ignore the factor 5.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 + -3c + 7a)' equal to zero and attempt to solve: Simplifying 2b + -3c + 7a = 0 Reorder the terms: 7a + 2b + -3c = 0 Solving 7a + 2b + -3c = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 7a + 2b + -2b + -3c = 0 + -2b Combine like terms: 2b + -2b = 0 7a + 0 + -3c = 0 + -2b 7a + -3c = 0 + -2b Remove the zero: 7a + -3c = -2b Add '3c' to each side of the equation. 7a + -3c + 3c = -2b + 3c Combine like terms: -3c + 3c = 0 7a + 0 = -2b + 3c 7a = -2b + 3c Divide each side by '7'. a = -0.2857142857b + 0.4285714286c Simplifying a = -0.2857142857b + 0.4285714286cSolution
a = {0, -0.2857142857b + 0.4285714286c}
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