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Simplifying 10z + -30 + -4z = 10(z + -5) * C Reorder the terms: -30 + 10z + -4z = 10(z + -5) * C Combine like terms: 10z + -4z = 6z -30 + 6z = 10(z + -5) * C Reorder the terms: -30 + 6z = 10(-5 + z) * C Reorder the terms for easier multiplication: -30 + 6z = 10C(-5 + z) -30 + 6z = (-5 * 10C + z * 10C) -30 + 6z = (-50C + 10zC) Solving -30 + 6z = -50C + 10zC Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-10zC' to each side of the equation. -30 + 6z + -10zC = -50C + 10zC + -10zC Combine like terms: 10zC + -10zC = 0 -30 + 6z + -10zC = -50C + 0 -30 + 6z + -10zC = -50C Add '30' to each side of the equation. -30 + 6z + 30 + -10zC = 30 + -50C Reorder the terms: -30 + 30 + 6z + -10zC = 30 + -50C Combine like terms: -30 + 30 = 0 0 + 6z + -10zC = 30 + -50C 6z + -10zC = 30 + -50C Reorder the terms: -30 + 50C + 6z + -10zC = 30 + -50C + -30 + 50C Reorder the terms: -30 + 50C + 6z + -10zC = 30 + -30 + -50C + 50C Combine like terms: 30 + -30 = 0 -30 + 50C + 6z + -10zC = 0 + -50C + 50C -30 + 50C + 6z + -10zC = -50C + 50C Combine like terms: -50C + 50C = 0 -30 + 50C + 6z + -10zC = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 25C + 3z + -5zC) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + 25C + 3z + -5zC)' equal to zero and attempt to solve: Simplifying -15 + 25C + 3z + -5zC = 0 Solving -15 + 25C + 3z + -5zC = 0 Move all terms containing z to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 25C + 3z + 15 + -5zC = 0 + 15 Reorder the terms: -15 + 15 + 25C + 3z + -5zC = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 25C + 3z + -5zC = 0 + 15 25C + 3z + -5zC = 0 + 15 Combine like terms: 0 + 15 = 15 25C + 3z + -5zC = 15 Add '-25C' to each side of the equation. 25C + 3z + -25C + -5zC = 15 + -25C Reorder the terms: 25C + -25C + 3z + -5zC = 15 + -25C Combine like terms: 25C + -25C = 0 0 + 3z + -5zC = 15 + -25C 3z + -5zC = 15 + -25C 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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