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Simplifying (3a + -4) * 2c(2b + 1) = 0 Reorder the terms: (-4 + 3a) * 2c(2b + 1) = 0 Reorder the terms: (-4 + 3a) * 2c(1 + 2b) = 0 Reorder the terms for easier multiplication: 2c(-4 + 3a)(1 + 2b) = 0 Multiply (-4 + 3a) * (1 + 2b) 2c(-4(1 + 2b) + 3a * (1 + 2b)) = 0 2c((1 * -4 + 2b * -4) + 3a * (1 + 2b)) = 0 2c((-4 + -8b) + 3a * (1 + 2b)) = 0 2c(-4 + -8b + (1 * 3a + 2b * 3a)) = 0 2c(-4 + -8b + (3a + 6ab)) = 0 Reorder the terms: 2c(-4 + 3a + 6ab + -8b) = 0 2c(-4 + 3a + 6ab + -8b) = 0 (-4 * 2c + 3a * 2c + 6ab * 2c + -8b * 2c) = 0 Reorder the terms: (12abc + 6ac + -16bc + -8c) = 0 (12abc + 6ac + -16bc + -8c) = 0 Solving 12abc + 6ac + -16bc + -8c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '16bc' to each side of the equation. 12abc + 6ac + -16bc + 16bc + -8c = 0 + 16bc Combine like terms: -16bc + 16bc = 0 12abc + 6ac + 0 + -8c = 0 + 16bc 12abc + 6ac + -8c = 0 + 16bc Remove the zero: 12abc + 6ac + -8c = 16bc Add '8c' to each side of the equation. 12abc + 6ac + -8c + 8c = 16bc + 8c Combine like terms: -8c + 8c = 0 12abc + 6ac + 0 = 16bc + 8c 12abc + 6ac = 16bc + 8c Reorder the terms: 12abc + 6ac + -16bc + -8c = 16bc + -16bc + 8c + -8c Combine like terms: 16bc + -16bc = 0 12abc + 6ac + -16bc + -8c = 0 + 8c + -8c 12abc + 6ac + -16bc + -8c = 8c + -8c Combine like terms: 8c + -8c = 0 12abc + 6ac + -16bc + -8c = 0 Factor out the Greatest Common Factor (GCF), '2c'. 2c(6ab + 3a + -8b + -4) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing a to the left, all other terms to the right. Add '-1c' to each side of the equation. c + -1c = 0 + -1c Remove the zero: 0 = -1c Simplifying 0 = -1c The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(6ab + 3a + -8b + -4)' equal to zero and attempt to solve: Simplifying 6ab + 3a + -8b + -4 = 0 Reorder the terms: -4 + 3a + 6ab + -8b = 0 Solving -4 + 3a + 6ab + -8b = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 3a + 6ab + 4 + -8b = 0 + 4 Reorder the terms: -4 + 4 + 3a + 6ab + -8b = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3a + 6ab + -8b = 0 + 4 3a + 6ab + -8b = 0 + 4 Combine like terms: 0 + 4 = 4 3a + 6ab + -8b = 4 Add '8b' to each side of the equation. 3a + 6ab + -8b + 8b = 4 + 8b Combine like terms: -8b + 8b = 0 3a + 6ab + 0 = 4 + 8b 3a + 6ab = 4 + 8b 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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