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Simplifying (1 + -1z)(5z + -9) = 0 Reorder the terms: (1 + -1z)(-9 + 5z) = 0 Multiply (1 + -1z) * (-9 + 5z) (1(-9 + 5z) + -1z * (-9 + 5z)) = 0 ((-9 * 1 + 5z * 1) + -1z * (-9 + 5z)) = 0 ((-9 + 5z) + -1z * (-9 + 5z)) = 0 (-9 + 5z + (-9 * -1z + 5z * -1z)) = 0 (-9 + 5z + (9z + -5z2)) = 0 Combine like terms: 5z + 9z = 14z (-9 + 14z + -5z2) = 0 Solving -9 + 14z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + 5z)(1 + -1z) = 0Subproblem 1
Set the factor '(-9 + 5z)' equal to zero and attempt to solve: Simplifying -9 + 5z = 0 Solving -9 + 5z = 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 + 5z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5z = 0 + 9 5z = 0 + 9 Combine like terms: 0 + 9 = 9 5z = 9 Divide each side by '5'. z = 1.8 Simplifying z = 1.8Subproblem 2
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 = 1Solution
z = {1.8, 1}
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