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Simplifying -4z(-4 + 5z) + -2z(9 + z) = 0 (-4 * -4z + 5z * -4z) + -2z(9 + z) = 0 (16z + -20z2) + -2z(9 + z) = 0 16z + -20z2 + (9 * -2z + z * -2z) = 0 16z + -20z2 + (-18z + -2z2) = 0 Reorder the terms: 16z + -18z + -20z2 + -2z2 = 0 Combine like terms: 16z + -18z = -2z -2z + -20z2 + -2z2 = 0 Combine like terms: -20z2 + -2z2 = -22z2 -2z + -22z2 = 0 Solving -2z + -22z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '-2z'. -2z(1 + 11z) = 0 Ignore the factor -2.Subproblem 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 '(1 + 11z)' equal to zero and attempt to solve: Simplifying 1 + 11z = 0 Solving 1 + 11z = 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 + 11z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 11z = 0 + -1 11z = 0 + -1 Combine like terms: 0 + -1 = -1 11z = -1 Divide each side by '11'. z = -0.09090909091 Simplifying z = -0.09090909091Solution
z = {0, -0.09090909091}
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