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Simplifying (8 + -1z)(5z + 7) = 0 Reorder the terms: (8 + -1z)(7 + 5z) = 0 Multiply (8 + -1z) * (7 + 5z) (8(7 + 5z) + -1z * (7 + 5z)) = 0 ((7 * 8 + 5z * 8) + -1z * (7 + 5z)) = 0 ((56 + 40z) + -1z * (7 + 5z)) = 0 (56 + 40z + (7 * -1z + 5z * -1z)) = 0 (56 + 40z + (-7z + -5z2)) = 0 Combine like terms: 40z + -7z = 33z (56 + 33z + -5z2) = 0 Solving 56 + 33z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (8 + -1z)(7 + 5z) = 0Subproblem 1
Set the factor '(8 + -1z)' equal to zero and attempt to solve: Simplifying 8 + -1z = 0 Solving 8 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1z = 0 + -8 -1z = 0 + -8 Combine like terms: 0 + -8 = -8 -1z = -8 Divide each side by '-1'. z = 8 Simplifying z = 8Subproblem 2
Set the factor '(7 + 5z)' equal to zero and attempt to solve: Simplifying 7 + 5z = 0 Solving 7 + 5z = 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 + 5z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5z = 0 + -7 5z = 0 + -7 Combine like terms: 0 + -7 = -7 5z = -7 Divide each side by '5'. z = -1.4 Simplifying z = -1.4Solution
z = {8, -1.4}
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