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Simplifying 5z(z + -2) + 3z(z + 4) = 0 Reorder the terms: 5z(-2 + z) + 3z(z + 4) = 0 (-2 * 5z + z * 5z) + 3z(z + 4) = 0 (-10z + 5z2) + 3z(z + 4) = 0 Reorder the terms: -10z + 5z2 + 3z(4 + z) = 0 -10z + 5z2 + (4 * 3z + z * 3z) = 0 -10z + 5z2 + (12z + 3z2) = 0 Reorder the terms: -10z + 12z + 5z2 + 3z2 = 0 Combine like terms: -10z + 12z = 2z 2z + 5z2 + 3z2 = 0 Combine like terms: 5z2 + 3z2 = 8z2 2z + 8z2 = 0 Solving 2z + 8z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z'. 2z(1 + 4z) = 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 + 4z)' equal to zero and attempt to solve: Simplifying 1 + 4z = 0 Solving 1 + 4z = 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 + 4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4z = 0 + -1 4z = 0 + -1 Combine like terms: 0 + -1 = -1 4z = -1 Divide each side by '4'. z = -0.25 Simplifying z = -0.25Solution
z = {0, -0.25}
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