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Simplifying (4z + -9)(2 + -1z) = 0 Reorder the terms: (-9 + 4z)(2 + -1z) = 0 Multiply (-9 + 4z) * (2 + -1z) (-9(2 + -1z) + 4z * (2 + -1z)) = 0 ((2 * -9 + -1z * -9) + 4z * (2 + -1z)) = 0 ((-18 + 9z) + 4z * (2 + -1z)) = 0 (-18 + 9z + (2 * 4z + -1z * 4z)) = 0 (-18 + 9z + (8z + -4z2)) = 0 Combine like terms: 9z + 8z = 17z (-18 + 17z + -4z2) = 0 Solving -18 + 17z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + 4z)(2 + -1z) = 0Subproblem 1
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 = 2.25Subproblem 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 = {2.25, 2}
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