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Simplifying 12z2 + -2z = 80 Reorder the terms: -2z + 12z2 = 80 Solving -2z + 12z2 = 80 Solving for variable 'z'. Reorder the terms: -80 + -2z + 12z2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + -2z + 12z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + -1z + 6z2) = 0 Factor a trinomial. 2((-5 + -2z)(8 + -3z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -2z)' equal to zero and attempt to solve: Simplifying -5 + -2z = 0 Solving -5 + -2z = 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 + -2z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2z = 0 + 5 -2z = 0 + 5 Combine like terms: 0 + 5 = 5 -2z = 5 Divide each side by '-2'. z = -2.5 Simplifying z = -2.5Subproblem 2
Set the factor '(8 + -3z)' equal to zero and attempt to solve: Simplifying 8 + -3z = 0 Solving 8 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3z = 0 + -8 -3z = 0 + -8 Combine like terms: 0 + -8 = -8 -3z = -8 Divide each side by '-3'. z = 2.666666667 Simplifying z = 2.666666667Solution
z = {-2.5, 2.666666667}
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