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Simplifying 5z(4z + 4) + 7z(3z + -3) = 0 Reorder the terms: 5z(4 + 4z) + 7z(3z + -3) = 0 (4 * 5z + 4z * 5z) + 7z(3z + -3) = 0 (20z + 20z2) + 7z(3z + -3) = 0 Reorder the terms: 20z + 20z2 + 7z(-3 + 3z) = 0 20z + 20z2 + (-3 * 7z + 3z * 7z) = 0 20z + 20z2 + (-21z + 21z2) = 0 Reorder the terms: 20z + -21z + 20z2 + 21z2 = 0 Combine like terms: 20z + -21z = -1z -1z + 20z2 + 21z2 = 0 Combine like terms: 20z2 + 21z2 = 41z2 -1z + 41z2 = 0 Solving -1z + 41z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-1 + 41z) = 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 '(-1 + 41z)' equal to zero and attempt to solve: Simplifying -1 + 41z = 0 Solving -1 + 41z = 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 + 41z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 41z = 0 + 1 41z = 0 + 1 Combine like terms: 0 + 1 = 1 41z = 1 Divide each side by '41'. z = 0.0243902439 Simplifying z = 0.0243902439Solution
z = {0, 0.0243902439}
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