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Simplifying 2(3a + -1b[3a + -1c(2a + 1) + 2ac] + -1c) = 0 Reorder the terms: 2(3a + -1b[3a + -1c(1 + 2a) + 2ac] + -1c) = 0 2(3a + -1b[3a + (1 * -1c + 2a * -1c) + 2ac] + -1c) = 0 Reorder the terms: 2(3a + -1b[3a + (-2ac + -1c) + 2ac] + -1c) = 0 2(3a + -1b[3a + (-2ac + -1c) + 2ac] + -1c) = 0 Reorder the terms: 2(3a + -1b[3a + -2ac + 2ac + -1c] + -1c) = 0 Combine like terms: -2ac + 2ac = 0 2(3a + -1b[3a + 0 + -1c] + -1c) = 0 2(3a + -1b[3a + -1c] + -1c) = 0 2(3a + [3a * -1b + -1c * -1b] + -1c) = 0 2(3a + [-3ab + 1bc] + -1c) = 0 (3a * 2 + -3ab * 2 + 1bc * 2 + -1c * 2) = 0 (6a + -6ab + 2bc + -2c) = 0 Solving 6a + -6ab + 2bc + -2c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2bc' to each side of the equation. 6a + -6ab + 2bc + -2bc + -2c = 0 + -2bc Combine like terms: 2bc + -2bc = 0 6a + -6ab + 0 + -2c = 0 + -2bc 6a + -6ab + -2c = 0 + -2bc Remove the zero: 6a + -6ab + -2c = -2bc Add '2c' to each side of the equation. 6a + -6ab + -2c + 2c = -2bc + 2c Combine like terms: -2c + 2c = 0 6a + -6ab + 0 = -2bc + 2c 6a + -6ab = -2bc + 2c Reorder the terms: 6a + -6ab + 2bc + -2c = -2bc + 2bc + 2c + -2c Combine like terms: -2bc + 2bc = 0 6a + -6ab + 2bc + -2c = 0 + 2c + -2c 6a + -6ab + 2bc + -2c = 2c + -2c Combine like terms: 2c + -2c = 0 6a + -6ab + 2bc + -2c = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3a + -3ab + bc + -1c) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3a + -3ab + bc + -1c)' equal to zero and attempt to solve: Simplifying 3a + -3ab + bc + -1c = 0 Solving 3a + -3ab + bc + -1c = 0 Move all terms containing a to the left, all other terms to the right. Add '-1bc' to each side of the equation. 3a + -3ab + bc + -1bc + -1c = 0 + -1bc Combine like terms: bc + -1bc = 0 3a + -3ab + 0 + -1c = 0 + -1bc 3a + -3ab + -1c = 0 + -1bc Remove the zero: 3a + -3ab + -1c = -1bc Add 'c' to each side of the equation. 3a + -3ab + -1c + c = -1bc + c Combine like terms: -1c + c = 0 3a + -3ab + 0 = -1bc + c 3a + -3ab = -1bc + c 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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