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Simplifying 5z(5z + 5) + 6z(5z + -6) = 0 Reorder the terms: 5z(5 + 5z) + 6z(5z + -6) = 0 (5 * 5z + 5z * 5z) + 6z(5z + -6) = 0 (25z + 25z2) + 6z(5z + -6) = 0 Reorder the terms: 25z + 25z2 + 6z(-6 + 5z) = 0 25z + 25z2 + (-6 * 6z + 5z * 6z) = 0 25z + 25z2 + (-36z + 30z2) = 0 Reorder the terms: 25z + -36z + 25z2 + 30z2 = 0 Combine like terms: 25z + -36z = -11z -11z + 25z2 + 30z2 = 0 Combine like terms: 25z2 + 30z2 = 55z2 -11z + 55z2 = 0 Solving -11z + 55z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '11z'. 11z(-1 + 5z) = 0 Ignore the factor 11.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 + 5z)' equal to zero and attempt to solve: Simplifying -1 + 5z = 0 Solving -1 + 5z = 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 + 5z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5z = 0 + 1 5z = 0 + 1 Combine like terms: 0 + 1 = 1 5z = 1 Divide each side by '5'. z = 0.2 Simplifying z = 0.2Solution
z = {0, 0.2}
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