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Simplifying 5z(4z + -4) + -2z(3z + -6) = 0 Reorder the terms: 5z(-4 + 4z) + -2z(3z + -6) = 0 (-4 * 5z + 4z * 5z) + -2z(3z + -6) = 0 (-20z + 20z2) + -2z(3z + -6) = 0 Reorder the terms: -20z + 20z2 + -2z(-6 + 3z) = 0 -20z + 20z2 + (-6 * -2z + 3z * -2z) = 0 -20z + 20z2 + (12z + -6z2) = 0 Reorder the terms: -20z + 12z + 20z2 + -6z2 = 0 Combine like terms: -20z + 12z = -8z -8z + 20z2 + -6z2 = 0 Combine like terms: 20z2 + -6z2 = 14z2 -8z + 14z2 = 0 Solving -8z + 14z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z'. 2z(-4 + 7z) = 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 '(-4 + 7z)' equal to zero and attempt to solve: Simplifying -4 + 7z = 0 Solving -4 + 7z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 7z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7z = 0 + 4 7z = 0 + 4 Combine like terms: 0 + 4 = 4 7z = 4 Divide each side by '7'. z = 0.5714285714 Simplifying z = 0.5714285714Solution
z = {0, 0.5714285714}
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