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Simplifying 6z2 + 7 = 17z Reorder the terms: 7 + 6z2 = 17z Solving 7 + 6z2 = 17z Solving for variable 'z'. Reorder the terms: 7 + -17z + 6z2 = 17z + -17z Combine like terms: 17z + -17z = 0 7 + -17z + 6z2 = 0 Factor a trinomial. (1 + -2z)(7 + -3z) = 0Subproblem 1
Set the factor '(1 + -2z)' equal to zero and attempt to solve: Simplifying 1 + -2z = 0 Solving 1 + -2z = 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 + -2z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2z = 0 + -1 -2z = 0 + -1 Combine like terms: 0 + -1 = -1 -2z = -1 Divide each side by '-2'. z = 0.5 Simplifying z = 0.5Subproblem 2
Set the factor '(7 + -3z)' equal to zero and attempt to solve: Simplifying 7 + -3z = 0 Solving 7 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3z = 0 + -7 -3z = 0 + -7 Combine like terms: 0 + -7 = -7 -3z = -7 Divide each side by '-3'. z = 2.333333333 Simplifying z = 2.333333333Solution
z = {0.5, 2.333333333}
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