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Simplifying 6a2(3a + 7b + -6c) = 0 (3a * 6a2 + 7b * 6a2 + -6c * 6a2) = 0 Reorder the terms: (42a2b + -36a2c + 18a3) = 0 (42a2b + -36a2c + 18a3) = 0 Solving 42a2b + -36a2c + 18a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6a2'. 6a2(7b + -6c + 3a) = 0 Ignore the factor 6.Subproblem 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 '(7b + -6c + 3a)' equal to zero and attempt to solve: Simplifying 7b + -6c + 3a = 0 Reorder the terms: 3a + 7b + -6c = 0 Solving 3a + 7b + -6c = 0 Move all terms containing a to the left, all other terms to the right. Add '-7b' to each side of the equation. 3a + 7b + -7b + -6c = 0 + -7b Combine like terms: 7b + -7b = 0 3a + 0 + -6c = 0 + -7b 3a + -6c = 0 + -7b Remove the zero: 3a + -6c = -7b Add '6c' to each side of the equation. 3a + -6c + 6c = -7b + 6c Combine like terms: -6c + 6c = 0 3a + 0 = -7b + 6c 3a = -7b + 6c Divide each side by '3'. a = -2.333333333b + 2c Simplifying a = -2.333333333b + 2cSolution
a = {0, -2.333333333b + 2c}
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