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Simplifying -1[3z2 + 3z + -1(2z2 + -5z)] + [(6z2 + -1[5z + -1z2]) + 5z2] = 0 Reorder the terms: -1[3z2 + 3z + -1(-5z + 2z2)] + [(6z2 + -1[5z + -1z2]) + 5z2] = 0 -1[3z2 + 3z + (-5z * -1 + 2z2 * -1)] + [(6z2 + -1[5z + -1z2]) + 5z2] = 0 -1[3z2 + 3z + (5z + -2z2)] + [(6z2 + -1[5z + -1z2]) + 5z2] = 0 Reorder the terms: -1[3z + 5z + 3z2 + -2z2] + [(6z2 + -1[5z + -1z2]) + 5z2] = 0 Combine like terms: 3z + 5z = 8z -1[8z + 3z2 + -2z2] + [(6z2 + -1[5z + -1z2]) + 5z2] = 0 Combine like terms: 3z2 + -2z2 = 1z2 -1[8z + 1z2] + [(6z2 + -1[5z + -1z2]) + 5z2] = 0 [8z * -1 + 1z2 * -1] + [(6z2 + -1[5z + -1z2]) + 5z2] = 0 [-8z + -1z2] + [(6z2 + -1[5z + -1z2]) + 5z2] = 0 -8z + -1z2 + [(6z2 + [5z * -1 + -1z2 * -1]) + 5z2] = 0 -8z + -1z2 + [(6z2 + [-5z + 1z2]) + 5z2] = 0 Reorder the terms: -8z + -1z2 + [(-5z + 6z2 + 1z2) + 5z2] = 0 Combine like terms: 6z2 + 1z2 = 7z2 -8z + -1z2 + [(-5z + 7z2) + 5z2] = 0 Remove parenthesis around (-5z + 7z2) -8z + -1z2 + [-5z + 7z2 + 5z2] = 0 Combine like terms: 7z2 + 5z2 = 12z2 -8z + -1z2 + [-5z + 12z2] = 0 Remove brackets around [-5z + 12z2] -8z + -1z2 + -5z + 12z2 = 0 Reorder the terms: -8z + -5z + -1z2 + 12z2 = 0 Combine like terms: -8z + -5z = -13z -13z + -1z2 + 12z2 = 0 Combine like terms: -1z2 + 12z2 = 11z2 -13z + 11z2 = 0 Solving -13z + 11z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-13 + 11z) = 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 + 11z)' equal to zero and attempt to solve: Simplifying -13 + 11z = 0 Solving -13 + 11z = 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 + 11z = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 11z = 0 + 13 11z = 0 + 13 Combine like terms: 0 + 13 = 13 11z = 13 Divide each side by '11'. z = 1.181818182 Simplifying z = 1.181818182Solution
z = {0, 1.181818182}
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