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Simplifying (9 + z)(4z + 7) = 0 Reorder the terms: (9 + z)(7 + 4z) = 0 Multiply (9 + z) * (7 + 4z) (9(7 + 4z) + z(7 + 4z)) = 0 ((7 * 9 + 4z * 9) + z(7 + 4z)) = 0 ((63 + 36z) + z(7 + 4z)) = 0 (63 + 36z + (7 * z + 4z * z)) = 0 (63 + 36z + (7z + 4z2)) = 0 Combine like terms: 36z + 7z = 43z (63 + 43z + 4z2) = 0 Solving 63 + 43z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (9 + z)(7 + 4z) = 0Subproblem 1
Set the factor '(9 + z)' equal to zero and attempt to solve: Simplifying 9 + z = 0 Solving 9 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + z = 0 + -9 z = 0 + -9 Combine like terms: 0 + -9 = -9 z = -9 Simplifying z = -9Subproblem 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 = {-9, -1.75}
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