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Simplifying 6a(b + 2) + 6c(b + 2) = 0 Reorder the terms: 6a(2 + b) + 6c(b + 2) = 0 (2 * 6a + b * 6a) + 6c(b + 2) = 0 (12a + 6ab) + 6c(b + 2) = 0 Reorder the terms: 12a + 6ab + 6c(2 + b) = 0 12a + 6ab + (2 * 6c + b * 6c) = 0 Reorder the terms: 12a + 6ab + (6bc + 12c) = 0 12a + 6ab + (6bc + 12c) = 0 Solving 12a + 6ab + 6bc + 12c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6bc' to each side of the equation. 12a + 6ab + 6bc + -6bc + 12c = 0 + -6bc Combine like terms: 6bc + -6bc = 0 12a + 6ab + 0 + 12c = 0 + -6bc 12a + 6ab + 12c = 0 + -6bc Remove the zero: 12a + 6ab + 12c = -6bc Add '-12c' to each side of the equation. 12a + 6ab + 12c + -12c = -6bc + -12c Combine like terms: 12c + -12c = 0 12a + 6ab + 0 = -6bc + -12c 12a + 6ab = -6bc + -12c Reorder the terms: 12a + 6ab + 6bc + 12c = -6bc + 6bc + -12c + 12c Combine like terms: -6bc + 6bc = 0 12a + 6ab + 6bc + 12c = 0 + -12c + 12c 12a + 6ab + 6bc + 12c = -12c + 12c Combine like terms: -12c + 12c = 0 12a + 6ab + 6bc + 12c = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(2a + ab + bc + 2c) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2a + ab + bc + 2c)' equal to zero and attempt to solve: Simplifying 2a + ab + bc + 2c = 0 Solving 2a + ab + bc + 2c = 0 Move all terms containing a to the left, all other terms to the right. Add '-1bc' to each side of the equation. 2a + ab + bc + -1bc + 2c = 0 + -1bc Combine like terms: bc + -1bc = 0 2a + ab + 0 + 2c = 0 + -1bc 2a + ab + 2c = 0 + -1bc Remove the zero: 2a + ab + 2c = -1bc Add '-2c' to each side of the equation. 2a + ab + 2c + -2c = -1bc + -2c Combine like terms: 2c + -2c = 0 2a + ab + 0 = -1bc + -2c 2a + ab = -1bc + -2c The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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