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Simplifying (5z + 4)(7 + -1z) = 0 Reorder the terms: (4 + 5z)(7 + -1z) = 0 Multiply (4 + 5z) * (7 + -1z) (4(7 + -1z) + 5z * (7 + -1z)) = 0 ((7 * 4 + -1z * 4) + 5z * (7 + -1z)) = 0 ((28 + -4z) + 5z * (7 + -1z)) = 0 (28 + -4z + (7 * 5z + -1z * 5z)) = 0 (28 + -4z + (35z + -5z2)) = 0 Combine like terms: -4z + 35z = 31z (28 + 31z + -5z2) = 0 Solving 28 + 31z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + -1z)(4 + 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 '(4 + 5z)' equal to zero and attempt to solve: Simplifying 4 + 5z = 0 Solving 4 + 5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5z = 0 + -4 5z = 0 + -4 Combine like terms: 0 + -4 = -4 5z = -4 Divide each side by '5'. z = -0.8 Simplifying z = -0.8Solution
z = {7, -0.8}
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