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Simplifying (4z + 3)(9 + -1z) = 0 Reorder the terms: (3 + 4z)(9 + -1z) = 0 Multiply (3 + 4z) * (9 + -1z) (3(9 + -1z) + 4z * (9 + -1z)) = 0 ((9 * 3 + -1z * 3) + 4z * (9 + -1z)) = 0 ((27 + -3z) + 4z * (9 + -1z)) = 0 (27 + -3z + (9 * 4z + -1z * 4z)) = 0 (27 + -3z + (36z + -4z2)) = 0 Combine like terms: -3z + 36z = 33z (27 + 33z + -4z2) = 0 Solving 27 + 33z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (9 + -1z)(3 + 4z) = 0Subproblem 1
Set the factor '(9 + -1z)' equal to zero and attempt to solve: Simplifying 9 + -1z = 0 Solving 9 + -1z = 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 + -1z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1z = 0 + -9 -1z = 0 + -9 Combine like terms: 0 + -9 = -9 -1z = -9 Divide each side by '-1'. z = 9 Simplifying z = 9Subproblem 2
Set the factor '(3 + 4z)' equal to zero and attempt to solve: Simplifying 3 + 4z = 0 Solving 3 + 4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4z = 0 + -3 4z = 0 + -3 Combine like terms: 0 + -3 = -3 4z = -3 Divide each side by '4'. z = -0.75 Simplifying z = -0.75Solution
z = {9, -0.75}
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