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Simplifying 20z2 = 80z + 100 Reorder the terms: 20z2 = 100 + 80z Solving 20z2 = 100 + 80z Solving for variable 'z'. Reorder the terms: -100 + -80z + 20z2 = 100 + 80z + -100 + -80z Reorder the terms: -100 + -80z + 20z2 = 100 + -100 + 80z + -80z Combine like terms: 100 + -100 = 0 -100 + -80z + 20z2 = 0 + 80z + -80z -100 + -80z + 20z2 = 80z + -80z Combine like terms: 80z + -80z = 0 -100 + -80z + 20z2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(-5 + -4z + z2) = 0 Factor a trinomial. 20((-1 + -1z)(5 + -1z)) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-1 + -1z)' equal to zero and attempt to solve: Simplifying -1 + -1z = 0 Solving -1 + -1z = 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 + -1z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1z = 0 + 1 -1z = 0 + 1 Combine like terms: 0 + 1 = 1 -1z = 1 Divide each side by '-1'. z = -1 Simplifying z = -1Subproblem 2
Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5Solution
z = {-1, 5}
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