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Simplifying 5z2 = -10z + -5 Reorder the terms: 5z2 = -5 + -10z Solving 5z2 = -5 + -10z Solving for variable 'z'. Reorder the terms: 5 + 10z + 5z2 = -5 + -10z + 5 + 10z Reorder the terms: 5 + 10z + 5z2 = -5 + 5 + -10z + 10z Combine like terms: -5 + 5 = 0 5 + 10z + 5z2 = 0 + -10z + 10z 5 + 10z + 5z2 = -10z + 10z Combine like terms: -10z + 10z = 0 5 + 10z + 5z2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 2z + z2) = 0 Factor a trinomial. 5((1 + z)(1 + z)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 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 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 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 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Solution
z = {-1, -1}
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