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Simplifying -10z2 + 45z + 6z + -54 = 0 Reorder the terms: -54 + 45z + 6z + -10z2 = 0 Combine like terms: 45z + 6z = 51z -54 + 51z + -10z2 = 0 Solving -54 + 51z + -10z2 = 0 Solving for variable 'z'. Factor a trinomial. (-18 + 5z)(3 + -2z) = 0Subproblem 1
Set the factor '(-18 + 5z)' equal to zero and attempt to solve: Simplifying -18 + 5z = 0 Solving -18 + 5z = 0 Move all terms containing z to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + 5z = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 5z = 0 + 18 5z = 0 + 18 Combine like terms: 0 + 18 = 18 5z = 18 Divide each side by '5'. z = 3.6 Simplifying z = 3.6Subproblem 2
Set the factor '(3 + -2z)' equal to zero and attempt to solve: Simplifying 3 + -2z = 0 Solving 3 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2z = 0 + -3 -2z = 0 + -3 Combine like terms: 0 + -3 = -3 -2z = -3 Divide each side by '-2'. z = 1.5 Simplifying z = 1.5Solution
z = {3.6, 1.5}
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