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Simplifying (1 + z)(4z + -9) = 0 Reorder the terms: (1 + z)(-9 + 4z) = 0 Multiply (1 + z) * (-9 + 4z) (1(-9 + 4z) + z(-9 + 4z)) = 0 ((-9 * 1 + 4z * 1) + z(-9 + 4z)) = 0 ((-9 + 4z) + z(-9 + 4z)) = 0 (-9 + 4z + (-9 * z + 4z * z)) = 0 (-9 + 4z + (-9z + 4z2)) = 0 Combine like terms: 4z + -9z = -5z (-9 + -5z + 4z2) = 0 Solving -9 + -5z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-1 + -1z)(9 + -4z) = 0Subproblem 1
Set the factor '(-1 + -1z)' equal to zero and attempt to solve: Simplifying -1 + -1z = 0 Solving -1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1z = 0 + 1 -1z = 0 + 1 Combine like terms: 0 + 1 = 1 -1z = 1 Divide each side by '-1'. z = -1 Simplifying z = -1Subproblem 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 = {-1, 2.25}
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