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Simplifying (5z + 6)(7 + -1z) = 0 Reorder the terms: (6 + 5z)(7 + -1z) = 0 Multiply (6 + 5z) * (7 + -1z) (6(7 + -1z) + 5z * (7 + -1z)) = 0 ((7 * 6 + -1z * 6) + 5z * (7 + -1z)) = 0 ((42 + -6z) + 5z * (7 + -1z)) = 0 (42 + -6z + (7 * 5z + -1z * 5z)) = 0 (42 + -6z + (35z + -5z2)) = 0 Combine like terms: -6z + 35z = 29z (42 + 29z + -5z2) = 0 Solving 42 + 29z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + -1z)(6 + 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 '(6 + 5z)' equal to zero and attempt to solve: Simplifying 6 + 5z = 0 Solving 6 + 5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5z = 0 + -6 5z = 0 + -6 Combine like terms: 0 + -6 = -6 5z = -6 Divide each side by '5'. z = -1.2 Simplifying z = -1.2Solution
z = {7, -1.2}
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