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Simplifying (9 + -1z)(4z + 1) = 0 Reorder the terms: (9 + -1z)(1 + 4z) = 0 Multiply (9 + -1z) * (1 + 4z) (9(1 + 4z) + -1z * (1 + 4z)) = 0 ((1 * 9 + 4z * 9) + -1z * (1 + 4z)) = 0 ((9 + 36z) + -1z * (1 + 4z)) = 0 (9 + 36z + (1 * -1z + 4z * -1z)) = 0 (9 + 36z + (-1z + -4z2)) = 0 Combine like terms: 36z + -1z = 35z (9 + 35z + -4z2) = 0 Solving 9 + 35z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (9 + -1z)(1 + 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 '(1 + 4z)' equal to zero and attempt to solve: Simplifying 1 + 4z = 0 Solving 1 + 4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4z = 0 + -1 4z = 0 + -1 Combine like terms: 0 + -1 = -1 4z = -1 Divide each side by '4'. z = -0.25 Simplifying z = -0.25Solution
z = {9, -0.25}
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