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Simplifying (6 + -1z)(4z + 7) = 0 Reorder the terms: (6 + -1z)(7 + 4z) = 0 Multiply (6 + -1z) * (7 + 4z) (6(7 + 4z) + -1z * (7 + 4z)) = 0 ((7 * 6 + 4z * 6) + -1z * (7 + 4z)) = 0 ((42 + 24z) + -1z * (7 + 4z)) = 0 (42 + 24z + (7 * -1z + 4z * -1z)) = 0 (42 + 24z + (-7z + -4z2)) = 0 Combine like terms: 24z + -7z = 17z (42 + 17z + -4z2) = 0 Solving 42 + 17z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (6 + -1z)(7 + 4z) = 0Subproblem 1
Set the factor '(6 + -1z)' equal to zero and attempt to solve: Simplifying 6 + -1z = 0 Solving 6 + -1z = 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 + -1z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1z = 0 + -6 -1z = 0 + -6 Combine like terms: 0 + -6 = -6 -1z = -6 Divide each side by '-1'. z = 6 Simplifying z = 6Subproblem 2
Set the factor '(7 + 4z)' equal to zero and attempt to solve: Simplifying 7 + 4z = 0 Solving 7 + 4z = 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 + 4z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4z = 0 + -7 4z = 0 + -7 Combine like terms: 0 + -7 = -7 4z = -7 Divide each side by '4'. z = -1.75 Simplifying z = -1.75Solution
z = {6, -1.75}
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