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Simplifying (5z + 1)(7 + -1z) = 0 Reorder the terms: (1 + 5z)(7 + -1z) = 0 Multiply (1 + 5z) * (7 + -1z) (1(7 + -1z) + 5z * (7 + -1z)) = 0 ((7 * 1 + -1z * 1) + 5z * (7 + -1z)) = 0 ((7 + -1z) + 5z * (7 + -1z)) = 0 (7 + -1z + (7 * 5z + -1z * 5z)) = 0 (7 + -1z + (35z + -5z2)) = 0 Combine like terms: -1z + 35z = 34z (7 + 34z + -5z2) = 0 Solving 7 + 34z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + -1z)(1 + 5z) = 0Subproblem 1
Set the factor '(7 + -1z)' equal to zero and attempt to solve: Simplifying 7 + -1z = 0 Solving 7 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1z = 0 + -7 -1z = 0 + -7 Combine like terms: 0 + -7 = -7 -1z = -7 Divide each side by '-1'. z = 7 Simplifying z = 7Subproblem 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 = {7, -0.2}
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