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Simplifying 3z2 + 2z = 4z2 + 4z Reorder the terms: 2z + 3z2 = 4z2 + 4z Reorder the terms: 2z + 3z2 = 4z + 4z2 Solving 2z + 3z2 = 4z + 4z2 Solving for variable 'z'. Reorder the terms: 2z + -4z + 3z2 + -4z2 = 4z + 4z2 + -4z + -4z2 Combine like terms: 2z + -4z = -2z -2z + 3z2 + -4z2 = 4z + 4z2 + -4z + -4z2 Combine like terms: 3z2 + -4z2 = -1z2 -2z + -1z2 = 4z + 4z2 + -4z + -4z2 Reorder the terms: -2z + -1z2 = 4z + -4z + 4z2 + -4z2 Combine like terms: 4z + -4z = 0 -2z + -1z2 = 0 + 4z2 + -4z2 -2z + -1z2 = 4z2 + -4z2 Combine like terms: 4z2 + -4z2 = 0 -2z + -1z2 = 0 Factor out the Greatest Common Factor (GCF), '-1z'. -1z(2 + z) = 0 Ignore the factor -1.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 '(2 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2Solution
z = {0, -2}
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