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Simplifying -1[3z2 + 5z + -1(2z2 + -3z)] + [(8z2 + -1[5z + -1z2]) + 4z2] = 0 Reorder the terms: -1[3z2 + 5z + -1(-3z + 2z2)] + [(8z2 + -1[5z + -1z2]) + 4z2] = 0 -1[3z2 + 5z + (-3z * -1 + 2z2 * -1)] + [(8z2 + -1[5z + -1z2]) + 4z2] = 0 -1[3z2 + 5z + (3z + -2z2)] + [(8z2 + -1[5z + -1z2]) + 4z2] = 0 Reorder the terms: -1[5z + 3z + 3z2 + -2z2] + [(8z2 + -1[5z + -1z2]) + 4z2] = 0 Combine like terms: 5z + 3z = 8z -1[8z + 3z2 + -2z2] + [(8z2 + -1[5z + -1z2]) + 4z2] = 0 Combine like terms: 3z2 + -2z2 = 1z2 -1[8z + 1z2] + [(8z2 + -1[5z + -1z2]) + 4z2] = 0 [8z * -1 + 1z2 * -1] + [(8z2 + -1[5z + -1z2]) + 4z2] = 0 [-8z + -1z2] + [(8z2 + -1[5z + -1z2]) + 4z2] = 0 -8z + -1z2 + [(8z2 + [5z * -1 + -1z2 * -1]) + 4z2] = 0 -8z + -1z2 + [(8z2 + [-5z + 1z2]) + 4z2] = 0 Reorder the terms: -8z + -1z2 + [(-5z + 8z2 + 1z2) + 4z2] = 0 Combine like terms: 8z2 + 1z2 = 9z2 -8z + -1z2 + [(-5z + 9z2) + 4z2] = 0 Remove parenthesis around (-5z + 9z2) -8z + -1z2 + [-5z + 9z2 + 4z2] = 0 Combine like terms: 9z2 + 4z2 = 13z2 -8z + -1z2 + [-5z + 13z2] = 0 Remove brackets around [-5z + 13z2] -8z + -1z2 + -5z + 13z2 = 0 Reorder the terms: -8z + -5z + -1z2 + 13z2 = 0 Combine like terms: -8z + -5z = -13z -13z + -1z2 + 13z2 = 0 Combine like terms: -1z2 + 13z2 = 12z2 -13z + 12z2 = 0 Solving -13z + 12z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-13 + 12z) = 0Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(-13 + 12z)' equal to zero and attempt to solve: Simplifying -13 + 12z = 0 Solving -13 + 12z = 0 Move all terms containing z to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 12z = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 12z = 0 + 13 12z = 0 + 13 Combine like terms: 0 + 13 = 13 12z = 13 Divide each side by '12'. z = 1.083333333 Simplifying z = 1.083333333Solution
z = {0, 1.083333333}
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