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Simplifying (3 + -1z)(2z + -9) = 0 Reorder the terms: (3 + -1z)(-9 + 2z) = 0 Multiply (3 + -1z) * (-9 + 2z) (3(-9 + 2z) + -1z * (-9 + 2z)) = 0 ((-9 * 3 + 2z * 3) + -1z * (-9 + 2z)) = 0 ((-27 + 6z) + -1z * (-9 + 2z)) = 0 (-27 + 6z + (-9 * -1z + 2z * -1z)) = 0 (-27 + 6z + (9z + -2z2)) = 0 Combine like terms: 6z + 9z = 15z (-27 + 15z + -2z2) = 0 Solving -27 + 15z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + 2z)(3 + -1z) = 0Subproblem 1
Set the factor '(-9 + 2z)' equal to zero and attempt to solve: Simplifying -9 + 2z = 0 Solving -9 + 2z = 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 + 2z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2z = 0 + 9 2z = 0 + 9 Combine like terms: 0 + 9 = 9 2z = 9 Divide each side by '2'. z = 4.5 Simplifying z = 4.5Subproblem 2
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 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 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Solution
z = {4.5, 3}
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