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Simplifying (4c + 2)(3x + 1) = 0 Reorder the terms: (2 + 4c)(3x + 1) = 0 Reorder the terms: (2 + 4c)(1 + 3x) = 0 Multiply (2 + 4c) * (1 + 3x) (2(1 + 3x) + 4c * (1 + 3x)) = 0 ((1 * 2 + 3x * 2) + 4c * (1 + 3x)) = 0 ((2 + 6x) + 4c * (1 + 3x)) = 0 (2 + 6x + (1 * 4c + 3x * 4c)) = 0 (2 + 6x + (4c + 12cx)) = 0 Reorder the terms: (2 + 4c + 12cx + 6x) = 0 (2 + 4c + 12cx + 6x) = 0 Solving 2 + 4c + 12cx + 6x = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 4c + 12cx + -2 + 6x = 0 + -2 Reorder the terms: 2 + -2 + 4c + 12cx + 6x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 4c + 12cx + 6x = 0 + -2 4c + 12cx + 6x = 0 + -2 Combine like terms: 0 + -2 = -2 4c + 12cx + 6x = -2 Add '-6x' to each side of the equation. 4c + 12cx + 6x + -6x = -2 + -6x Combine like terms: 6x + -6x = 0 4c + 12cx + 0 = -2 + -6x 4c + 12cx = -2 + -6x Reorder the terms: 2 + 4c + 12cx + 6x = -2 + -6x + 2 + 6x Reorder the terms: 2 + 4c + 12cx + 6x = -2 + 2 + -6x + 6x Combine like terms: -2 + 2 = 0 2 + 4c + 12cx + 6x = 0 + -6x + 6x 2 + 4c + 12cx + 6x = -6x + 6x Combine like terms: -6x + 6x = 0 2 + 4c + 12cx + 6x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 2c + 6cx + 3x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 2c + 6cx + 3x)' equal to zero and attempt to solve: Simplifying 1 + 2c + 6cx + 3x = 0 Solving 1 + 2c + 6cx + 3x = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2c + 6cx + -1 + 3x = 0 + -1 Reorder the terms: 1 + -1 + 2c + 6cx + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2c + 6cx + 3x = 0 + -1 2c + 6cx + 3x = 0 + -1 Combine like terms: 0 + -1 = -1 2c + 6cx + 3x = -1 Add '-3x' to each side of the equation. 2c + 6cx + 3x + -3x = -1 + -3x Combine like terms: 3x + -3x = 0 2c + 6cx + 0 = -1 + -3x 2c + 6cx = -1 + -3x 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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