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Simplifying 3p + 10z = 2p(1.5 + 10z) 3p + 10z = (1.5 * 2p + 10z * 2p) 3p + 10z = (3p + 20pz) Add '-3p' to each side of the equation. 3p + -3p + 10z = 3p + -3p + 20pz Combine like terms: 3p + -3p = 0 0 + 10z = 3p + -3p + 20pz 10z = 3p + -3p + 20pz Combine like terms: 3p + -3p = 0 10z = 0 + 20pz 10z = 20pz Solving 10z = 20pz Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-20pz' to each side of the equation. -20pz + 10z = 20pz + -20pz Combine like terms: 20pz + -20pz = 0 -20pz + 10z = 0 Factor out the Greatest Common Factor (GCF), '10z'. 10z(-2p + 1) = 0 Ignore the factor 10.Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(-2p + 1)' equal to zero and attempt to solve: Simplifying -2p + 1 = 0 Reorder the terms: 1 + -2p = 0 Solving 1 + -2p = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2p = 0 + -1 -2p = 0 + -1 Combine like terms: 0 + -1 = -1 -2p = -1 Add '2p' to each side of the equation. -2p + 2p = -1 + 2p Combine like terms: -2p + 2p = 0 0 = -1 + 2p Simplifying 0 = -1 + 2p The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
z = {0}
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