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Simplifying 4(5c + 8d) + -24 = -20c(d) (5c * 4 + 8d * 4) + -24 = -20c(d) (20c + 32d) + -24 = -20c(d) Reorder the terms: -24 + 20c + 32d = -20c(d) Multiply c * d -24 + 20c + 32d = -20cd Solving -24 + 20c + 32d = -20cd Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '20cd' to each side of the equation. -24 + 20c + 20cd + 32d = -20cd + 20cd Combine like terms: -20cd + 20cd = 0 -24 + 20c + 20cd + 32d = 0 Add '24' to each side of the equation. -24 + 20c + 20cd + 24 + 32d = 0 + 24 Reorder the terms: -24 + 24 + 20c + 20cd + 32d = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 20c + 20cd + 32d = 0 + 24 20c + 20cd + 32d = 0 + 24 Combine like terms: 0 + 24 = 24 20c + 20cd + 32d = 24 Add '-32d' to each side of the equation. 20c + 20cd + 32d + -32d = 24 + -32d Combine like terms: 32d + -32d = 0 20c + 20cd + 0 = 24 + -32d 20c + 20cd = 24 + -32d Reorder the terms: -24 + 20c + 20cd + 32d = 24 + -32d + -24 + 32d Reorder the terms: -24 + 20c + 20cd + 32d = 24 + -24 + -32d + 32d Combine like terms: 24 + -24 = 0 -24 + 20c + 20cd + 32d = 0 + -32d + 32d -24 + 20c + 20cd + 32d = -32d + 32d Combine like terms: -32d + 32d = 0 -24 + 20c + 20cd + 32d = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + 5c + 5cd + 8d) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + 5c + 5cd + 8d)' equal to zero and attempt to solve: Simplifying -6 + 5c + 5cd + 8d = 0 Solving -6 + 5c + 5cd + 8d = 0 Move all terms containing c to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 5c + 5cd + 6 + 8d = 0 + 6 Reorder the terms: -6 + 6 + 5c + 5cd + 8d = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 5c + 5cd + 8d = 0 + 6 5c + 5cd + 8d = 0 + 6 Combine like terms: 0 + 6 = 6 5c + 5cd + 8d = 6 Add '-8d' to each side of the equation. 5c + 5cd + 8d + -8d = 6 + -8d Combine like terms: 8d + -8d = 0 5c + 5cd + 0 = 6 + -8d 5c + 5cd = 6 + -8d 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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