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Simplifying 5z(4z + -3) + -7z(4z + 4) = 0 Reorder the terms: 5z(-3 + 4z) + -7z(4z + 4) = 0 (-3 * 5z + 4z * 5z) + -7z(4z + 4) = 0 (-15z + 20z2) + -7z(4z + 4) = 0 Reorder the terms: -15z + 20z2 + -7z(4 + 4z) = 0 -15z + 20z2 + (4 * -7z + 4z * -7z) = 0 -15z + 20z2 + (-28z + -28z2) = 0 Reorder the terms: -15z + -28z + 20z2 + -28z2 = 0 Combine like terms: -15z + -28z = -43z -43z + 20z2 + -28z2 = 0 Combine like terms: 20z2 + -28z2 = -8z2 -43z + -8z2 = 0 Solving -43z + -8z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '-1z'. -1z(43 + 8z) = 0 Ignore the factor -1.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 '(43 + 8z)' equal to zero and attempt to solve: Simplifying 43 + 8z = 0 Solving 43 + 8z = 0 Move all terms containing z to the left, all other terms to the right. Add '-43' to each side of the equation. 43 + -43 + 8z = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 8z = 0 + -43 8z = 0 + -43 Combine like terms: 0 + -43 = -43 8z = -43 Divide each side by '8'. z = -5.375 Simplifying z = -5.375Solution
z = {0, -5.375}
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