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Simplifying 8z(10z + 1) + (10z + 1) = 0 Reorder the terms: 8z(1 + 10z) + (10z + 1) = 0 (1 * 8z + 10z * 8z) + (10z + 1) = 0 (8z + 80z2) + (10z + 1) = 0 Reorder the terms: 8z + 80z2 + (1 + 10z) = 0 Remove parenthesis around (1 + 10z) 8z + 80z2 + 1 + 10z = 0 Reorder the terms: 1 + 8z + 10z + 80z2 = 0 Combine like terms: 8z + 10z = 18z 1 + 18z + 80z2 = 0 Solving 1 + 18z + 80z2 = 0 Solving for variable 'z'. Factor a trinomial. (1 + 8z)(1 + 10z) = 0Subproblem 1
Set the factor '(1 + 8z)' equal to zero and attempt to solve: Simplifying 1 + 8z = 0 Solving 1 + 8z = 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 + 8z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8z = 0 + -1 8z = 0 + -1 Combine like terms: 0 + -1 = -1 8z = -1 Divide each side by '8'. z = -0.125 Simplifying z = -0.125Subproblem 2
Set the factor '(1 + 10z)' equal to zero and attempt to solve: Simplifying 1 + 10z = 0 Solving 1 + 10z = 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 + 10z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 10z = 0 + -1 10z = 0 + -1 Combine like terms: 0 + -1 = -1 10z = -1 Divide each side by '10'. z = -0.1 Simplifying z = -0.1Solution
z = {-0.125, -0.1}
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