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Simplifying (4z + -9)(3 + -1z) = 0 Reorder the terms: (-9 + 4z)(3 + -1z) = 0 Multiply (-9 + 4z) * (3 + -1z) (-9(3 + -1z) + 4z * (3 + -1z)) = 0 ((3 * -9 + -1z * -9) + 4z * (3 + -1z)) = 0 ((-27 + 9z) + 4z * (3 + -1z)) = 0 (-27 + 9z + (3 * 4z + -1z * 4z)) = 0 (-27 + 9z + (12z + -4z2)) = 0 Combine like terms: 9z + 12z = 21z (-27 + 21z + -4z2) = 0 Solving -27 + 21z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-3 + z)(9 + -4z) = 0Subproblem 1
Set the factor '(-3 + z)' equal to zero and attempt to solve: Simplifying -3 + z = 0 Solving -3 + z = 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 + z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + z = 0 + 3 z = 0 + 3 Combine like terms: 0 + 3 = 3 z = 3 Simplifying z = 3Subproblem 2
Set the factor '(9 + -4z)' equal to zero and attempt to solve: Simplifying 9 + -4z = 0 Solving 9 + -4z = 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 + -4z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4z = 0 + -9 -4z = 0 + -9 Combine like terms: 0 + -9 = -9 -4z = -9 Divide each side by '-4'. z = 2.25 Simplifying z = 2.25Solution
z = {3, 2.25}
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