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Simplifying (5z + 1)(2 + z) = 0 Reorder the terms: (1 + 5z)(2 + z) = 0 Multiply (1 + 5z) * (2 + z) (1(2 + z) + 5z * (2 + z)) = 0 ((2 * 1 + z * 1) + 5z * (2 + z)) = 0 ((2 + 1z) + 5z * (2 + z)) = 0 (2 + 1z + (2 * 5z + z * 5z)) = 0 (2 + 1z + (10z + 5z2)) = 0 Combine like terms: 1z + 10z = 11z (2 + 11z + 5z2) = 0 Solving 2 + 11z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + z)(1 + 5z) = 0Subproblem 1
Set the factor '(2 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2Subproblem 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 = {-2, -0.2}
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