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Simplifying (2z + -9)(4 + z) = 0 Reorder the terms: (-9 + 2z)(4 + z) = 0 Multiply (-9 + 2z) * (4 + z) (-9(4 + z) + 2z * (4 + z)) = 0 ((4 * -9 + z * -9) + 2z * (4 + z)) = 0 ((-36 + -9z) + 2z * (4 + z)) = 0 (-36 + -9z + (4 * 2z + z * 2z)) = 0 (-36 + -9z + (8z + 2z2)) = 0 Combine like terms: -9z + 8z = -1z (-36 + -1z + 2z2) = 0 Solving -36 + -1z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-4 + -1z)(9 + -2z) = 0Subproblem 1
Set the factor '(-4 + -1z)' equal to zero and attempt to solve: Simplifying -4 + -1z = 0 Solving -4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1z = 0 + 4 -1z = 0 + 4 Combine like terms: 0 + 4 = 4 -1z = 4 Divide each side by '-1'. z = -4 Simplifying z = -4Subproblem 2
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 = 4.5Solution
z = {-4, 4.5}
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