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Simplifying (4z + -9)(6 + z) = 0 Reorder the terms: (-9 + 4z)(6 + z) = 0 Multiply (-9 + 4z) * (6 + z) (-9(6 + z) + 4z * (6 + z)) = 0 ((6 * -9 + z * -9) + 4z * (6 + z)) = 0 ((-54 + -9z) + 4z * (6 + z)) = 0 (-54 + -9z + (6 * 4z + z * 4z)) = 0 (-54 + -9z + (24z + 4z2)) = 0 Combine like terms: -9z + 24z = 15z (-54 + 15z + 4z2) = 0 Solving -54 + 15z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-6 + -1z)(9 + -4z) = 0Subproblem 1
Set the factor '(-6 + -1z)' equal to zero and attempt to solve: Simplifying -6 + -1z = 0 Solving -6 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1z = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1z = 0 + 6 -1z = 0 + 6 Combine like terms: 0 + 6 = 6 -1z = 6 Divide each side by '-1'. z = -6 Simplifying z = -6Subproblem 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 = {-6, 2.25}
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