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