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Simplifying [(9z2 + -1[5z + -1z2]) + 4z2] = 0 [(9z2 + [5z * -1 + -1z2 * -1]) + 4z2] = 0 [(9z2 + [-5z + 1z2]) + 4z2] = 0 Reorder the terms: [(-5z + 9z2 + 1z2) + 4z2] = 0 Combine like terms: 9z2 + 1z2 = 10z2 [(-5z + 10z2) + 4z2] = 0 Remove parenthesis around (-5z + 10z2) [-5z + 10z2 + 4z2] = 0 Combine like terms: 10z2 + 4z2 = 14z2 [-5z + 14z2] = 0 Remove brackets around [-5z + 14z2] -5z + 14z2 = 0 Solving -5z + 14z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-5 + 14z) = 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 '(-5 + 14z)' equal to zero and attempt to solve: Simplifying -5 + 14z = 0 Solving -5 + 14z = 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 + 14z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 14z = 0 + 5 14z = 0 + 5 Combine like terms: 0 + 5 = 5 14z = 5 Divide each side by '14'. z = 0.3571428571 Simplifying z = 0.3571428571Solution
z = {0, 0.3571428571}
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