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Simplifying (2 + -1z)(2z + -9) = 0 Reorder the terms: (2 + -1z)(-9 + 2z) = 0 Multiply (2 + -1z) * (-9 + 2z) (2(-9 + 2z) + -1z * (-9 + 2z)) = 0 ((-9 * 2 + 2z * 2) + -1z * (-9 + 2z)) = 0 ((-18 + 4z) + -1z * (-9 + 2z)) = 0 (-18 + 4z + (-9 * -1z + 2z * -1z)) = 0 (-18 + 4z + (9z + -2z2)) = 0 Combine like terms: 4z + 9z = 13z (-18 + 13z + -2z2) = 0 Solving -18 + 13z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + 2z)(2 + -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 '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Solution
z = {4.5, 2}
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